Editing Hubble's law

{{short description|Observation in physical cosmology}}
[[File:Raisinbread.gif|thumb|upright=1.3|An analogy for explaining Hubble's law, using [[raisin]]s in a rising loaf of bread in place of galaxies. If a raisin is twice as far away from a place as another raisin, then the farther raisin would move away from that place twice as quickly.]]
{{Cosmology|expansion}}
'''Hubble's law''', also known as the '''Hubble–Lemaître law''',<ref>{{cite press release |date=29 October 2018 |title=IAU members vote to recommend renaming the Hubble law as the Hubble–Lemaître law |url=https://www.iau.org/news/pressreleases/detail/iau1812/?lang |publisher=[[International Astronomical Union|IAU]] |access-date=2018-10-29}}</ref> is the observation in [[physical cosmology]] that [[galaxies]] are moving away from Earth at speeds proportional to their distance. In other words, the farther a galaxy is from the Earth, the faster it moves away. A galaxy's [[recessional velocity]] is typically determined by measuring its [[redshift]], a shift in the frequency of [[light]] emitted by the galaxy.

The discovery of Hubble's law is attributed to work published by [[Edwin Hubble]] in 1929,<ref>{{cite journal |last1=van den Bergh |first1=S. |title=The Curious Case of Lemaitre's Equation No. 24 |journal=[[Journal of the Royal Astronomical Society of Canada]] |volume=105 |issue=4 |date=August 2011 |page=151 |arxiv=1106.1195 |bibcode=2011JRASC.105..151V |url=https://www.rasc.ca/jrasc-2011-08 }}</ref><ref>{{cite journal |last1=Nussbaumer |first1=H. |last2=Bieri |first2=L. | author2-link = Lydia Bieri |date=2011 |title=Who discovered the expanding universe? |journal=[[The Observatory (journal)|The Observatory]] |volume=131 |issue=6 |pages=394–398 |arxiv=1107.2281 |bibcode=2011Obs...131..394N }}</ref><ref>{{cite book |last1=Way |first1=M.J. |date=2013 |chapter=Dismantling Hubble's Legacy? |chapter-url=https://www.aspbooks.org/publications/471/097.pdf |title=Origins of the Expanding Universe: 1912-1932 |editor=Michael J. Way |editor2=Deidre Hunter |publisher=Astronomical Society of the Pacific |series=[[ASP Conference Series]] |volume=471 |pages=97–132 |arxiv=1301.7294 |bibcode=2013ASPC..471...97W }}</ref> but the notion of the universe expanding at a calculable rate was first derived from [[general relativity]] equations in 1922 by [[Alexander Friedmann]]. The [[Friedmann equations]] showed the universe might be expanding, and presented the expansion speed if that were the case.<ref>{{cite journal |last1=Friedman |first1=A. |date=December 1922 |title=Über die Krümmung des Raumes |journal=Zeitschrift für Physik |language=de |volume=10 |issue=1 |pages=377–386 |bibcode=1922ZPhy...10..377F |doi=10.1007/BF01332580 |s2cid=125190902}}. (English translation in {{cite journal |last1=Friedman |first1=A. |date=December 1999 |title=On the Curvature of Space |journal=General Relativity and Gravitation |volume=31 |issue=12 |pages=1991–2000 |bibcode=1999GReGr..31.1991F |doi=10.1023/A:1026751225741 |s2cid=122950995}})</ref> Before Hubble, astronomer [[Carl Wilhelm Wirtz]] had, in 1922<ref name="Wirtz-1922">{{Cite journal |last1=Wirtz |first1=C. W. |date       = April 1922 |title      = Einiges zur Statistik der Radialbewegungen von Spiralnebeln und Kugelsternhaufen |journal    = Astronomische Nachrichten |volume     = 215 |issue=17 |pages=349–354 |bibcode    = 1922AN....215..349W |doi        = 10.1002/asna.19212151703|url=https://zenodo.org/record/1424934 }}</ref> and 1924,<ref name="Wirtz-1924">{{cite journal |last1=Wirtz |first1=C. W. |year=1924 |title=De Sitters Kosmologie und die Radialbewegungen der Spiralnebel |journal=[[Astronomische Nachrichten]] |volume=222|issue=5306|pages=21–26 |bibcode=1924AN....222...21W |doi=10.1002/asna.19242220203}}</ref> deduced with his own data that galaxies that appeared smaller and dimmer had larger redshifts and thus that more distant galaxies recede faster from the observer. In 1927, [[Georges Lemaître]] concluded that the universe might be expanding by noting the proportionality of the recessional velocity of distant bodies to their respective distances. He estimated a value for this ratio, which—after Hubble confirmed cosmic expansion and determined a more precise value for it two years later—became known as the Hubble constant.<ref name="NYT-20170220" /><ref>{{cite journal |last=Lemaître |first=G. |author-link=Georges Lemaître |date=1927 |title=Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques |journal=Annales de la Société Scientifique de Bruxelles A |language=fr |volume=47 |pages=49–59 |bibcode=1927ASSB...47...49L}} Partially translated to English in {{Cite journal |last=Lemaître |first=G. |date=1931 |title=Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=91 |issue=5 |pages=483–490 |bibcode=1931MNRAS..91..483L |doi=10.1093/mnras/91.5.483 |doi-access=free}}</ref><ref name="Livio">{{cite journal|last=Livio|first=M.|date=2011|title=Lost in translation: Mystery of the missing text solved|journal=[[Nature (journal)|Nature]]|volume=479|issue=7372|pages=171–173|bibcode=2011Natur.479..171L|doi=10.1038/479171a|pmid=22071745|s2cid=203468083|doi-access=free}}</ref><ref>{{cite journal|last1=Livio|first1=M.|last2=Riess|first2=A.|date=2013|title=Measuring the Hubble constant|journal=[[Physics Today]]|volume=66|issue=10|pages=41–47|bibcode=2013PhT....66j..41L|doi=10.1063/PT.3.2148}}</ref><ref name=":1">{{cite journal |last=Hubble |first=E. |date=1929 |title=A relation between distance and radial velocity among extra-galactic nebulae |journal=[[Proceedings of the National Academy of Sciences]] |volume=15 |issue=3 |pages=168–173 |bibcode=1929PNAS...15..168H |doi=10.1073/pnas.15.3.168 |pmc=522427 |pmid=16577160 |doi-access=free}}</ref> Hubble inferred the recession velocity of the objects from their [[redshift]]s, many of which were earlier measured and related to velocity by [[Vesto Slipher]] in 1917.<ref>{{cite journal|last1=Slipher|first1=V.M.|date=1917|title=Radial velocity observations of spiral nebulae|journal=The Observatory|volume=40|pages=304–306|bibcode=1917Obs....40..304S}}</ref><ref name="MS_Longair2">{{cite book|last=Longair|first=M. S.|url=https://archive.org/details/cosmiccenturyhis0000long|title=The Cosmic Century|date=2006|publisher=[[Cambridge University Press]]|isbn=978-0-521-47436-8|page=[https://archive.org/details/cosmiccenturyhis0000long/page/109 109]|url-access=registration}}</ref><ref>{{cite book |last1=Nussbaumer |first1=Harry |chapter=Slipher's redshifts as support for de Sitter's model and the discovery of the dynamic universe |chapter-url=https://www.aspbooks.org/publications/471/025.pdf |title=Origins of the Expanding Universe: 1912–1932 |date=2013 |series=[[ASP Conference Series]] |volume=471 |editor=Michael J. Way |editor2=Deidre Hunter |publisher=Astronomical Society of the Pacific |pages=25–38 |arxiv=1303.1814}}</ref> Combining Slipher's velocities with [[Henrietta Swan Leavitt]]'s intergalactic distance calculations and methodology allowed Hubble to better calculate an expansion rate for the universe.<ref>{{cite web |title=1912: Henrietta Leavitt Discovers the Distance Key |url=https://cosmology.carnegiescience.edu/timeline/1912.html#:~:text=Henrietta%20Swan%20Leavitt.,are%20far%20beyond%20that%20distance. |website=Everyday Cosmology |access-date=18 February 2024}}</ref>

Hubble's law is considered the first observational basis for the [[expansion of the universe]], and is one of the pieces of evidence most often cited in support of the [[Big Bang]] model.<ref name="NYT-20170220">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Cosmos Controversy: The Universe Is Expanding, but How Fast? |url=https://www.nytimes.com/2017/02/20/science/hubble-constant-universe-expanding-speed.html |date=20 February 2017 |work=[[New York Times]] |access-date=21 February 2017 }}</ref><ref name="Coles">{{cite book |editor-last=Coles |editor-first=P. |date=2001 |title=Routledge Critical Dictionary of the New Cosmology |url=https://books.google.com/books?id=BgNGWVr5yhIC&pg=PA202 |page=202 |isbn=978-0-203-16457-0 |publisher=[[Routledge]] }}</ref> The motion of astronomical objects due solely to this expansion is known as the '''Hubble flow'''.<ref>{{cite web |title=Hubble Flow |url=http://astronomy.swin.edu.au/cosmos/h/hubble+flow |website=The Swinburne Astronomy Online Encyclopedia of Astronomy |publisher=[[Swinburne University of Technology]] |access-date=2013-05-14 }}</ref> It is described by the equation {{math|''v'' {{=}} ''H''<sub>0</sub>''D''}}, with {{math|''H''<sub>0</sub>}} the constant of proportionality—the '''Hubble constant'''—between the "proper distance" {{mvar|D}} to a galaxy (which can change over time, unlike the [[Comoving and proper distances|comoving distance]]) and its speed of separation {{mvar|v}}, i.e. the [[derivative]] of proper distance with respect to the [[cosmic time]] coordinate.{{efn|See ''{{section link|Comoving and proper distances#Uses of the proper distance}}'' for discussion of the subtleties of this definition of ''velocity.''}} Though the Hubble constant {{math|''H''<sub>0</sub>}} is constant at any given moment in time, the '''Hubble parameter''' {{mvar|H}}, of which the Hubble constant is the current value, varies with time, so the term ''constant'' is sometimes thought of as somewhat of a misnomer.<ref name="NYT-20190225">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Have Dark Forces Been Messing With the Cosmos? – Axions? Phantom energy? Astrophysicists scramble to patch a hole in the universe, rewriting cosmic history in the process. |url=https://www.nytimes.com/2019/02/25/science/cosmos-hubble-dark-energy.html |date=25 February 2019 |work=[[The New York Times]] |access-date=26 February 2019 }}</ref><ref>{{cite book|last1=O'Raifeartaigh|first1=Cormac|chapter=The Contribution of V.M. Slipher to the discovery of the expanding universe |chapter-url=https://www.aspbooks.org/publications/471/049.pdf |title=Origins of the Expanding Universe: 1912-1932|date=2013|publisher=Astronomical Society of the Pacific|series=[[ASP Conference Series]]|volume=471|pages=49–62|arxiv=1212.5499}}</ref>

The Hubble constant is most frequently quoted in [[kilometre|km]]/[[second|s]]/[[Parsec#Megaparsecs and gigaparsecs|Mpc]], which gives the speed of a galaxy {{convert|1|Mpc|km|sigfig=3}} away as {{nobr|70 km/s}}. Simplifying the units of the generalized form reveals that {{math|''H''<sub>0</sub>}} specifies a [[frequency]] (SI unit: [[Hertz|s<sup>−1</sup>]]), leading the reciprocal of {{math|''H''<sub>0</sub>}} to be known as the [[#Hubble time|Hubble time]] (14.4 billion years). The Hubble constant can also be stated as a relative rate of expansion. In this form {{math|''H''<sub>0</sub>}}&nbsp;= 7%/[[Year#Abbreviations for "years_ago"|Gyr]], meaning that, at the current rate of expansion, it takes one billion years for an unbound structure to grow by 7%.

== Discovery ==
[[File:Three steps to the Hubble constant.jpg|thumb|upright=2.2|Three steps to the Hubble constant<ref>{{cite web|title=Three steps to the Hubble constant|url=https://www.spacetelescope.org/images/opo1812a/|website=www.spacetelescope.org|access-date=26 February 2018}}</ref>]]

A decade before Hubble made his observations, a number of [[physicists]] and [[mathematician]]s had established a consistent theory of an expanding universe by using [[Einstein field equations]] of [[general relativity]]. Applying the most [[Cosmological principle|general principles]] to the nature of the [[universe]] yielded a [[Dynamics (mechanics)|dynamic]] solution that conflicted with the then-prevalent notion of a [[static universe]].

=== Slipher's observations ===
In 1912, [[Vesto M. Slipher]] measured the first [[Doppler shift]] of a "[[spiral nebula]]" (the obsolete term for spiral galaxies) and soon discovered that almost all such objects were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was [[Shapley–Curtis debate|highly controversial]] whether or not these nebulae were "island universes" outside the Milky Way galaxy.<ref>{{cite journal |last=Slipher |first=V. M. |date=1913 |title=The Radial Velocity of the Andromeda Nebula |journal=[[Lowell Observatory Bulletin]] |volume=1 |issue=8 |pages=56–57 |bibcode=1913LowOB...2...56S }}</ref><ref>{{Cite journal |last=Slipher |first=V. M. |date=1915 |title=Spectrographic Observations of Nebulae |journal=[[Popular Astronomy (US magazine)|Popular Astronomy]] |volume=23 |pages=21–24 |bibcode=1915PA.....23...21S }}</ref>

=== FLRW equations ===
{{Main|Friedmann–Lemaître–Robertson–Walker metric}}
In 1922, [[Alexander Friedmann]] derived his Friedmann equations from [[Einstein field equations]], showing that the universe might expand at a rate calculable by the equations.<ref>{{Cite journal |last=Friedman |first=A. |date=1922 |title=Über die Krümmung des Raumes |journal=[[Zeitschrift für Physik]] |language=de |volume=10 |issue=1 |pages=377–386 |bibcode=1922ZPhy...10..377F |doi=10.1007/BF01332580 |s2cid=125190902}} Translated to English in {{Cite journal |last1=Friedmann |first1=A. |date=1999 |title=On the Curvature of Space |journal=[[General Relativity and Gravitation]] |volume=31 |issue=12 |pages=1991–2000 |bibcode=1999GReGr..31.1991F |doi=10.1023/A:1026751225741 |s2cid=122950995}}</ref> The parameter used by Friedmann is known today as the [[Scale factor (cosmology)|scale factor]] and can be considered as a [[Scale invariance|scale invariant]] form of the [[Proportionality (mathematics)|proportionality constant]] of Hubble's law. Georges Lemaître independently found a similar solution in his 1927 paper discussed in the following section. The Friedmann equations are derived by inserting the [[Friedmann–Lemaître–Robertson–Walker metric|metric for a homogeneous and isotropic universe]] into Einstein's field equations for a fluid with a given [[density]] and [[pressure]]. This idea of an expanding spacetime would eventually lead to the [[Big Bang]] and [[Steady State Theory|Steady State]] theories of [[cosmology]].

=== Lemaître's equation ===
In 1927, two years before Hubble published his own article, the Belgian priest and astronomer Georges Lemaître was the first to publish research deriving what is now known as Hubble's law. According to the Canadian astronomer [[Sidney van den Bergh]], "the 1927 discovery of the expansion of the universe by Lemaître was published in French in a low-impact journal. In the 1931 high-impact English translation of this article, a critical equation was changed by omitting reference to what is now known as the Hubble constant."<ref>{{cite journal|last1=van den Bergh|first1=Sydney|title=The Curious Case of Lemaître's Equation No. 24|journal=Journal of the Royal Astronomical Society of Canada|volume=105|issue=4|page=151|arxiv=1106.1195|year=2011|bibcode=2011JRASC.105..151V}}</ref> It is now known that the alterations in the translated paper were carried out by Lemaître himself.<ref name = Livio /><ref>{{cite book|last1=Block|first1=David|title='Georges Lemaitre and Stigler's law of eponymy' in Georges Lemaître: Life, Science and Legacy|date=2012|publisher=Springer|pages=89–96|edition=Holder and Mitton}}</ref>

=== Shape of the universe ===
Before the advent of modern cosmology, there was considerable talk about the size and [[shape of the universe]]. In 1920, the [[Great Debate (astronomy)|Shapley–Curtis debate]] took place between [[Harlow Shapley]] and [[Heber Doust Curtis|Heber D. Curtis]] over this issue. Shapley argued for a small universe the size of the Milky Way galaxy, and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.

=== Cepheid variable stars outside the Milky Way ===
Edwin Hubble did most of his professional astronomical observing work at [[Mount Wilson Observatory]],<ref>{{cite journal | last = Sandage | first = Allan | title = Edwin Hubble 1889–1953 | date = December 1989 | journal = Journal of the Royal Astronomical Society of Canada | volume = 83 | issue = 6 | pages = 351–362| bibcode = 1989JRASC..83..351S }}</ref> home to the world's most powerful telescope at the time. His observations of [[Cepheid variable]] stars in "spiral nebulae" enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be called ''nebulae'', and it was only gradually that the term ''galaxies'' replaced it.

=== Combining redshifts with distance measurements ===

[[File:Hubble constant.JPG|thumb|upright=1.45|Fit of [[#Redshift velocity|redshift velocities]] to Hubble's law.<ref name="Keel">{{cite book |last=Keel |first=W. C. |date=2007 |title=The Road to Galaxy Formation |url=https://books.google.com/books?id=BUgJGypUYF0C&pg=PA7 |pages=7–8 |edition=2nd |publisher=[[Springer (publisher)|Springer]] |isbn=978-3-540-72534-3 }}</ref> Various estimates for the [[#Determining the Hubble constant|Hubble constant]] exist.]]

The velocities and distances that appear in Hubble's law are not directly measured. The velocities are inferred from the redshift {{math|1=''z'' = ∆''λ''/''λ''}} of radiation and distance is inferred from brightness. Hubble sought to correlate brightness with parameter {{mvar|z}}.

Combining his measurements of galaxy distances with Vesto Slipher and [[Milton Humason]]'s measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there was considerable [[variance|scatter]] (now known to be caused by [[peculiar velocity|peculiar velocities]]—the 'Hubble flow' is used to refer to the region of space far enough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500&nbsp;(km/s)/Mpc (much higher than the currently accepted value due to errors in his distance calibrations; see [[cosmic distance ladder]] for details).<ref name=damnh/>

==== Hubble diagram ====
Hubble's law can be easily depicted in a "Hubble diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer.<ref>{{cite journal |last=Kirshner |first=R. P. |date=2003 |title=Hubble's diagram and cosmic expansion |journal=[[Proceedings of the National Academy of Sciences]] |volume=101 |issue=1 |pages=8–13 |bibcode=2004PNAS..101....8K |doi=10.1073/pnas.2536799100 |pmid=14695886 |pmc=314128 |doi-access=free }}</ref> A straight line of positive slope on this diagram is the visual depiction of Hubble's law.

=== Cosmological constant abandoned ===
{{main|Cosmological constant}}
After Hubble's discovery was published, [[Albert Einstein]] abandoned his work on the [[cosmological constant]], a [[Term (logic)|term]] he had inserted into his equations of general relativity to coerce them into producing the static solution he previously considered the correct state of the universe. The Einstein equations in their simplest form model either an expanding or contracting universe, so Einstein introduced the constant to counter expansion or contraction and lead to a static and flat universe.<ref name="mapcc">{{cite web |title=What is a Cosmological Constant? |url=http://map.gsfc.nasa.gov/universe/uni_accel.html |publisher=[[Goddard Space Flight Center]] |access-date=2013-10-17 }}</ref> After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "greatest mistake".<ref name=mapcc /> On its own, general relativity could predict the expansion of the universe, which (through [[Tests of general relativity|observations]] such as the [[Gravitational lens|bending of light by large masses]], or the [[Perihelion precession of Mercury|precession of the orbit of Mercury]]) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

In 1931, Einstein went to Mount Wilson Observatory to thank Hubble for providing the observational basis for modern cosmology.<ref>{{cite book |last=Isaacson |first=W. |date=2007 |title=Einstein: His Life and Universe |url=https://archive.org/details/einsteinhislifeu0000isaa |url-access=registration |page=[https://archive.org/details/einsteinhislifeu0000isaa/page/n395 354] |publisher=[[Simon & Schuster]] |isbn=978-0-7432-6473-0 }}</ref>

The cosmological constant has regained attention in recent decades as a hypothetical explanation for [[dark energy]].<ref>{{cite web |date=28 November 2007 |title=Einstein's Biggest Blunder? Dark Energy May Be Consistent With Cosmological Constant |url=https://www.sciencedaily.com/releases/2007/11/071127142128.htm |website=[[Science Daily]] |access-date=2013-06-02 }}</ref>

{{anchor|redshift}}

== Interpretation ==
[[File:Velocity-redshift.JPG|thumb|upright=1.4|A variety of possible recessional velocity vs. redshift functions including the simple linear relation {{math|1=''v'' = ''cz''}}; a variety of possible shapes from theories related to general relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts.<ref name="D&L">{{cite journal |last1=Davis |first1=T. M. |last2=Lineweaver |first2=C. H. |date=2001 |title=Superluminal Recessional Velocities |journal=[[AIP Conference Proceedings]] |volume=555 |pages=348–351 |arxiv=astro-ph/0011070 |bibcode=2001AIPC..555..348D |doi=10.1063/1.1363540 |citeseerx=10.1.1.254.1810 |s2cid=118876362 }}</ref>]]
The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between [[recessional velocity]] and redshift, yields a straightforward mathematical expression for Hubble's law as follows:

<math display="block">v = H_0 \, D</math>

where
* {{mvar|v}} is the recessional velocity, typically expressed in km/s.
* {{math|''H''<sub>0</sub>}} is Hubble's constant and corresponds to the value of {{mvar|H}} (often termed the '''Hubble parameter''' which is a value that is [[time-variant system|time dependent]] and which can be expressed in terms of the [[Scale factor (cosmology)|scale factor]]) in the Friedmann equations taken at the time of observation denoted by the subscript {{math|0}}. This value is the same throughout the universe for a given [[comoving time#Comoving coordinates|comoving time]].
* {{mvar|D}} is the proper distance (which can change over time, unlike the [[comoving distance]], which is constant) from the [[galaxy]] to the observer, measured in [[mega-|mega]] [[parsec]]s (Mpc), in the 3-space defined by given [[cosmological time]]. (Recession velocity is just {{math|1=''v'' = ''dD/dt''}}).

Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted and is not established except for small redshifts.

For distances {{mvar|D}} larger than the radius of the [[Hubble sphere]] {{math|''r''<sub>HS</sub>}}, objects recede at a rate faster than the [[speed of light]] (''See'' [[Comoving distance#Uses of the proper distance|Uses of the proper distance]] for a discussion of the significance of this):

<math display="block">r_\text{HS} = \frac{c}{H_0} \ . </math>

Since the Hubble "constant" is a constant only in space, not in time, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today.<ref name=Keel/> Current evidence suggests that the expansion of the universe is accelerating (''see'' [[Accelerating universe]]), meaning that for any given galaxy, the recession velocity {{mvar|dD/dt}} is increasing over time as the galaxy moves to greater and greater distances; however, the Hubble parameter is actually thought to be decreasing with time, meaning that if we were to look at some {{em|fixed}} distance {{mvar|D}} and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones.<ref>{{cite web|title=Is the universe expanding faster than the speed of light?|url=http://curious.astro.cornell.edu/question.php?number=575|website=Ask an Astronomer at Cornell University|access-date=5 June 2015|archive-url=https://web.archive.org/web/20031123150109/http://curious.astro.cornell.edu/question.php?number=575|archive-date=23 November 2003}}</ref>

=== Redshift velocity and recessional velocity ===
Redshift can be measured by determining the wavelength of a known transition, such as hydrogen α-lines for distant quasars, and finding the fractional shift compared to a stationary reference. Thus, redshift is a quantity unambiguously acquired from observation. Care is required, however, in translating these to recessional velocities: for small redshift values, a linear relation of redshift to recessional velocity applies, but more generally the redshift-distance law is nonlinear, meaning the co-relation must be derived specifically for each given model and epoch.<ref name="Harrison">{{cite journal |last=Harrison |first=E. |date=1992 |title=The redshift-distance and velocity-distance laws |journal=[[The Astrophysical Journal]] |volume=403 |pages=28–31 | bibcode=1993ApJ...403...28H |doi=10.1086/172179|doi-access=free }}</ref>

==== Redshift velocity ====
The redshift {{mvar|z}} is often described as a ''redshift velocity'', which is the recessional velocity that would produce the same redshift {{em|if}} it were caused by a linear [[Doppler effect]] (which, however, is not the case, as the velocities involved are too large to use a non-relativistic formula for Doppler shift). This redshift velocity can easily exceed the speed of light.<ref name="Madsen">{{cite book |last=Madsen |first=M. S. |date=1995 |title=The Dynamic Cosmos |url=https://books.google.com/books?id=_2GeJxVvyFMC&pg=PA35 |page=35 |publisher=[[CRC Press]] |isbn=978-0-412-62300-4 }}</ref> In other words, to determine the redshift velocity {{math|''v''<sub>rs</sub>}}, the relation:

<math display="block"> v_\text{rs} \equiv cz,</math>

is used.<ref name="Dekel">{{cite book |last1=Dekel |first1=A. |last2=Ostriker |first2=J. P. |date=1999 |title=Formation of Structure in the Universe |url=https://books.google.com/books?id=yAroX6tx-l0C&pg=PA164 |page=164 |publisher=[[Cambridge University Press]] |isbn=978-0-521-58632-0 }}</ref><ref name="Padmanabhan">{{cite book |last=Padmanabhan |first=T. |date=1993 |title=Structure formation in the universe | url=https://books.google.com/books?id=AJlOVBRZJtIC&pg=PA58 |page=58 |publisher=[[Cambridge University Press]] |isbn=978-0-521-42486-8 }}</ref> That is, there is {{em|no fundamental difference}} between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called [[Relativistic Doppler effect|Fizeau–Doppler formula]]<ref name="Sartori">{{cite book |last=Sartori |first=L. |date=1996 |title=Understanding Relativity |page=163, Appendix 5B |publisher=[[University of California Press]] |isbn=978-0-520-20029-6 }}</ref>

<math display="block">z = \frac{\lambda_\text{o}}{\lambda_\text{e}}-1 = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}-1 \approx \frac{v}{c}.</math>

Here, {{math|''λ''<sub>o</sub>}}, {{math|''λ''<sub>e</sub>}} are the observed and emitted wavelengths respectively. The "redshift velocity" {{math|''v''<sub>rs</sub>}} is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity. Next, the connection between redshift or redshift velocity and recessional velocity is discussed.<ref name="L_Sartori">{{cite book|last=Sartori |first=L. |date=1996 |title=Understanding Relativity |pages=304–305 |publisher=[[University of California Press]] |isbn=978-0-520-20029-6 }}</ref>

==== Recessional velocity ====

Suppose {{math|''R''(''t'')}} is called the ''scale factor'' of the universe, and increases as the universe expands in a manner that depends upon the [[Physical cosmology|cosmological model]] selected. Its meaning is that all measured proper distances {{math|''D''(''t'')}} between co-moving points increase proportionally to {{mvar|R}}. (The co-moving points are not moving relative to their local environments.) In other words:

<math display="block">\frac {D(t)}{D(t_0)} = \frac{R(t)}{R(t_0)},</math>

where {{math|''t''<sub>0</sub>}} is some reference time.<ref>Matts Roos, ''Introduction to Cosmology''</ref> If light is emitted from a galaxy at time {{math|''t''<sub>e</sub>}} and received by us at {{math|''t''<sub>0</sub>}}, it is redshifted due to the expansion of the universe, and this redshift {{mvar|z}} is simply:

<math display="block">z = \frac {R(t_0)}{R(t_\text{e})} - 1. </math>

Suppose a galaxy is at distance {{mvar|D}}, and this distance changes with time at a rate {{mvar|d<sub>t</sub>D}}. We call this rate of recession the "recession velocity" {{math|''v''<sub>r</sub>}}:

<math display="block">v_\text{r} = d_tD = \frac {d_tR}{R} D. </math>

We now define the Hubble constant as

<math display="block">H \equiv \frac{d_tR}{R}, </math>

and discover the Hubble law:

<math display="block"> v_\text{r} = H D. </math>

From this perspective, Hubble's law is a fundamental relation between (i) the recessional velocity associated with the expansion of the universe and (ii) the distance to an object; the connection between redshift and distance is a crutch used to connect Hubble's law with observations. This law can be related to redshift {{mvar|z}} approximately by making a [[Taylor series]] expansion:

<math display="block"> z = \frac {R(t_0)}{R(t_e)} - 1 \approx \frac {R(t_0)} {R(t_0)\left(1+(t_e-t_0)H(t_0)\right)}-1 \approx (t_0-t_e)H(t_0), </math>

If the distance is not too large, all other complications of the model become small corrections, and the time interval is simply the distance divided by the speed of light:

<math display="block"> z \approx (t_0-t_\text{e})H(t_0) \approx \frac {D}{c} H(t_0), </math>

or

<math display="block"> cz \approx D H(t_0) = v_r. </math>

According to this approach, the relation {{math|1=''cz'' = ''v''<sub>r</sub>}} is an approximation valid at low redshifts, to be replaced by a relation at large redshifts that is model-dependent. See [[#redshift|velocity-redshift figure]].

=== Observability of parameters ===
Strictly speaking, neither {{mvar|v}} nor {{mvar|D}} in the formula are directly observable, because they are properties {{em|now}} of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it.

For relatively nearby galaxies (redshift {{mvar|z}} much less than one), {{mvar|v}} and {{mvar|D}} will not have changed much, and {{mvar|v}} can be estimated using the formula {{math|1= v = zc}} where {{mvar|c}} is the speed of light. This gives the empirical relation found by Hubble.

For distant galaxies, {{mvar|v}} (or {{mvar|D}}) cannot be calculated from {{mvar|z}} without specifying a detailed model for how {{mvar|H}} changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation: {{math|(1 + ''z'')}} is the factor by which the universe has expanded while the photon was traveling towards the observer.

=== Expansion velocity vs. peculiar velocity ===
In using Hubble's law to determine distances, only the velocity due to the expansion of the universe can be used. Since gravitationally interacting galaxies move relative to each other independent of the expansion of the universe,<ref name="AM-20170818">{{cite web |last=Scharping |first=Nathaniel |title=Gravitational Waves Show How Fast The Universe is Expanding |url=http://www.astronomy.com/news/2017/10/gravitational-waves-show-how-fast-the-universe-is-expanding |date=18 October 2017 |website=[[Astronomy (magazine)|Astronomy]] |access-date=18 October 2017 }}</ref> these relative velocities, called peculiar velocities, need to be accounted for in the application of Hubble's law. Such peculiar velocities give rise to [[redshift-space distortions]].

=== Time-dependence of Hubble parameter ===

The parameter {{mvar|H}} is commonly called the "Hubble constant", but that is a misnomer since it is constant in space only at a fixed time; it varies with time in nearly all cosmological models, and all observations of far distant objects are also observations into the distant past, when the "constant" had a different value. "Hubble parameter" is a more correct term, with {{math|''H''{{sub|0}}}} denoting the present-day value.

Another common source of confusion is that the accelerating universe does {{em|not}} imply that the Hubble parameter is actually increasing with time; since {{nowrap|<math> H(t) \equiv \dot{a}(t)/a(t) </math>,}} in most accelerating models <math>a</math> increases relatively faster than {{nowrap|<math>\dot{a}</math>,}} so {{mvar|H}} decreases with time. (The recession velocity of one chosen galaxy does increase, but different galaxies passing a sphere of fixed radius cross the sphere more slowly at later times.)

On defining the dimensionless [[deceleration parameter]] {{nowrap|<math display="inline"> q \equiv - \frac {\ddot{a}\, a} {\dot{a}^2} </math>,}} it follows that

<math display="block"> \frac{dH}{dt} = -H^2 (1+q) </math>

From this it is seen that the Hubble parameter is decreasing with time, unless {{math|''q'' < -1}}; the latter can only occur if the universe contains [[phantom energy]], regarded as theoretically somewhat improbable.

However, in the standard [[Lambda-CDM model|Lambda cold dark matter model]] (Lambda-CDM or ΛCDM model), {{mvar|q}} will tend to −1 from above in the distant future as the cosmological constant becomes increasingly dominant over matter; this implies that {{mvar|H}} will approach from above to a constant value of ≈&nbsp;57&nbsp;(km/s)/Mpc, and the scale factor of the universe will then grow exponentially in time.

=== Idealized Hubble's law ===
The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional [[Cartesian coordinate system|Cartesian]]/Newtonian coordinate space, which, considered as a [[metric space]], is entirely [[Cosmological principle|homogeneous and isotropic]] (properties do not vary with location or direction). Simply stated, the theorem is this:

{{blockquote|Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.}}

In fact, this applies to non-Cartesian spaces as long as they are locally homogeneous and isotropic, specifically to the negatively and positively curved spaces frequently considered as cosmological models (see [[shape of the universe]]).

An observation stemming from this theorem is that seeing objects recede from us on Earth is not an indication that Earth is near to a center from which the expansion is occurring, but rather that {{em|every}} observer in an expanding universe will see objects receding from them.

=== Ultimate fate and age of the universe ===
[[Image:Friedmann universes.svg|thumb|upright=1.9|The [[age of the universe|age]] and [[ultimate fate of the universe]] can be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterized by values of density parameters ({{math|Ω<sub>M</sub>}} for [[matter]] and {{math|Ω<sub>Λ</sub>}} for dark energy).<br>A '''closed universe''' with {{math|Ω<sub>M</sub> > 1}} and {{math|1= Ω<sub>Λ</sub> = 0}} comes to an end in a [[Big Crunch]] and is considerably younger than its Hubble age.<br>An '''open universe''' with {{math|Ω<sub>M</sub> ≤ 1}} and {{math|1= Ω<sub>Λ</sub> = 0}} expands forever and has an age that is closer to its Hubble age. For the accelerating universe with nonzero {{math|Ω<sub>Λ</sub>}} that we inhabit, the age of the universe is coincidentally very close to the Hubble age.]]

The value of the Hubble parameter changes over time, either increasing or decreasing depending on the value of the so-called [[deceleration parameter]] {{mvar|q}}, which is defined by

<math display="block">q = -\left(1+\frac{\dot H}{H^2}\right).</math>

In a universe with a deceleration parameter equal to zero, it follows that {{math|1= ''H'' = 1/''t''}}, where {{mvar|t}} is the time since the Big Bang. A non-zero, time-dependent value of {{mvar|q}} simply requires [[integral|integration]] of the Friedmann equations backwards from the present time to the time when the [[particle horizon|comoving horizon]] size was zero.

It was long thought that {{mvar|q}} was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than {{math|1/''H''}} (which is about 14 billion years). For instance, a value for {{mvar|q}} of 1/2 (once favoured by most theorists) would give the age of the universe as {{math|2/(3''H'')}}. The discovery in 1998 that {{mvar|q}} is apparently negative means that the universe could actually be older than {{math|1/''H''}}. However, estimates of the [[age of the universe]] are very close to {{math|1/''H''}}.

=== Olbers' paradox ===
{{Main|Olbers' paradox}}
The expansion of space summarized by the Big Bang interpretation of Hubble's law is relevant to the old conundrum known as [[Olbers' paradox]]: If the universe were [[Infinity|infinite]] in size, [[static universe|static]], and filled with a uniform distribution of [[star]]s, then every line of sight in the sky would end on a star, and the sky would be as [[brightness|bright]] as the surface of a star. However, the night sky is largely dark.<ref name="Chase_etal_2004">{{cite web |last1=Chase |first1=S. I. |last2=Baez |first2=J. C. |date=2004 |title=Olbers' Paradox |url=http://math.ucr.edu/home/baez/physics/Relativity/GR/olbers.html |website=The Original Usenet Physics FAQ |access-date=2013-10-17}}</ref><ref name="Asimov1974">{{cite book |last=Asimov |first=I. |date=1974 |chapter=The Black of Night |title=Asimov on Astronomy |publisher=[[Doubleday (publisher)|Doubleday]] |isbn=978-0-385-04111-9 |chapter-url-access=registration |chapter-url=https://archive.org/details/asimovonastronom00isaa |url-access=registration |url=https://archive.org/details/asimovonastronom00isaa }}</ref>

Since the 17th&nbsp;century, astronomers and other thinkers have proposed many possible ways to resolve this paradox, but the currently accepted resolution depends in part on the Big Bang theory, and in part on the Hubble expansion: in a universe that existed for a finite amount of time, only the light of a finite number of stars has had enough time to reach us, and the paradox is resolved. Additionally, in an expanding universe, distant objects recede from us, which causes the light emanated from them to be redshifted and diminished in brightness by the time we see it.<ref name=Chase_etal_2004/><ref name=Asimov1974/>

=== Dimensionless Hubble constant ===
Instead of working with Hubble's constant, a common practice is to introduce the '''dimensionless Hubble constant''', usually denoted by {{mvar|h}} and commonly referred to as "little h",<ref name=damnh>{{cite journal |last=Croton |first=Darren J. |date=14 October 2013 |title=Damn You, Little h! (Or, Real-World Applications of the Hubble Constant Using Observed and Simulated Data) |journal=Publications of the Astronomical Society of Australia |volume=30 |url=https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/damn-you-little-h-or-real-world-applications-of-the-hubble-constant-using-observed-and-simulated-data/EB4B786F4500F897A589C3ED980C17F5 |doi=10.1017/pasa.2013.31 |arxiv=1308.4150 |bibcode=2013PASA...30...52C |s2cid=119257465 |access-date=8 December 2021}}</ref> then to write Hubble's constant {{math|''H''<sub>0</sub>}} as {{math|''h'' × 100 km⋅[[second|s]]<sup>−1</sup>⋅[[Parsec|Mpc]]<sup>−1</sup>}}, all the relative uncertainty of the true value of {{math|''H''<sub>0</sub>}} being then relegated to {{mvar|h}}.<ref>{{cite book |last=Peebles |first=P. J. E. |date=1993 |title=Principles of Physical Cosmology |publisher=[[Princeton University Press]] | isbn=978-0-691-07428-3}}</ref> The dimensionless Hubble constant is often used when giving distances that are calculated from redshift {{mvar|z}} using the formula {{math|1= ''d'' ≈ {{sfrac|''c''|''H''<sub>0</sub>}} × ''z''}}. Since {{math|''H''<sub>0</sub>}} is not precisely known, the distance is expressed as:

<math display="block">cz/H_0\approx(2998\times z)\text{ Mpc }h^{-1}</math>

In other words, one calculates 2998 × {{mvar|z}} and one gives the units as Mpc&nbsp;{{math|''h''{{sup|-1}}}} or {{math|''h''{{sup|-1}}}}&nbsp;Mpc.

Occasionally a reference value other than 100 may be chosen, in which case a subscript is presented after {{mvar|h}} to avoid confusion; e.g. {{math|''h''{{sub|70}}}} denotes {{math|1= ''H''{{sub|0}} = 70 ''h''{{sub|70}}}}&nbsp;{{val||ul=km/s|upl=Mpc}}, which implies {{math|1= ''h''{{sub|70}} = ''h'' / 0.7}}.

This should not be confused with the [[Dimensionless physical constant|dimensionless value]] of Hubble's constant, usually expressed in terms of [[Planck units]], obtained by multiplying {{math|''H''<sub>0</sub>}} by {{val|1.75|e=-63}} (from definitions of parsec and [[Planck time|{{math|''t''<sub>P</sub>}}]]), for example for {{math|1= ''H''{{sub|0}} = 70}}, a Planck unit version of {{val|1.2|e=-61}} is obtained.

=== Acceleration of the expansion ===
{{Main|Accelerating expansion of the universe}}
A value for {{mvar|q}} measured from [[standard candle]] observations of [[Type Ia supernova]]e, which was determined in 1998 to be negative, surprised many astronomers with the implication that the expansion of the universe is currently "accelerating"<ref>{{cite journal |last=Perlmutter |first=S. |date=2003 |title=Supernovae, Dark Energy, and the Accelerating Universe |url=http://www.supernova.lbl.gov/PhysicsTodayArticle.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.supernova.lbl.gov/PhysicsTodayArticle.pdf |archive-date=2022-10-09 |url-status=live |journal=[[Physics Today]] |volume=56 |issue=4 |pages=53–60 |bibcode= 2003PhT....56d..53P |doi=10.1063/1.1580050 |citeseerx=10.1.1.77.7990 }}</ref> (although the Hubble factor is still decreasing with time, as mentioned above in the [[#Interpretation|Interpretation]] section; see the articles on [[dark energy]] and the ΛCDM model).

== Derivation of the Hubble parameter ==
{{More citations needed section|date=March 2014}}

Start with the [[Friedmann equations|Friedmann equation]]:

<math display="block">H^2 \equiv \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho - \frac{kc^2}{a^2}+ \frac{\Lambda c^2}{3},</math>

where {{mvar|H}} is the Hubble parameter, {{mvar|a}} is the [[scale factor (universe)|scale factor]], {{mvar|G}} is the [[gravitational constant]], {{mvar|k}} is the normalised spatial curvature of the universe and equal to −1, 0, or 1, and {{math|Λ}} is the cosmological constant.

=== Matter-dominated universe (with a cosmological constant) ===

If the universe is [[Matter-dominated era|matter-dominated]], then the mass density of the universe {{mvar|ρ}} can be taken to include just matter so

<math display="block">\rho = \rho_m(a) = \frac{\rho_{m_{0}}}{a^3},</math>

where {{math|''ρ''{{sub|''m''{{sub|0}}}}}} is the density of matter today. From the Friedmann equation and thermodynamic principles we know for non-relativistic particles that their mass density decreases proportional to the inverse volume of the universe, so the equation above must be true. We can also define (see [[density parameter]] for {{math|Ω{{sub|''m''}}}})

<math display="block">\begin{align}
\rho_c &= \frac{3 H_0^2}{8 \pi G}; \\
\Omega_m &\equiv \frac{\rho_{m_{0}}}{\rho_c} = \frac{8 \pi G}{3 H_0^2}\rho_{m_{0}};
\end{align}</math>

therefore:

<math display="block">\rho=\frac{\rho_c \Omega_m}{a^3}.</math>

Also, by definition,
<math display="block">\begin{align}
\Omega_k &\equiv \frac{-kc^2}{(a_0H_0)^2} \\
\Omega_{\Lambda} &\equiv \frac{\Lambda c^2}{3H_0^2},
\end{align}</math>

where the subscript {{math|0}} refers to the values today, and {{math|1= ''a''{{sub|0}} = 1}}. Substituting all of this into the Friedmann equation at the start of this section and replacing {{mvar|a}} with {{math|1= ''a'' = 1/(1+''z'')}} gives

<math display="block">H^2(z)= H_0^2 \left( \Omega_m (1+z)^{3} + \Omega_k (1+z)^{2} + \Omega_{\Lambda} \right).</math>

=== Matter- and dark energy-dominated universe ===

If the universe is both matter-dominated and dark energy-dominated, then the above equation for the Hubble parameter will also be a function of the [[equation of state (cosmology)|equation of state of dark energy]]. So now:

<math display="block">\rho = \rho_m (a)+\rho_{de}(a),</math>

where {{mvar|ρ{{sub|de}}}} is the mass density of the dark energy. By definition, an equation of state in cosmology is {{math|1= ''P'' = ''wρc''{{sup|2}}}}, and if this is substituted into the fluid equation, which describes how the mass density of the universe evolves with time, then

<math display="block">\begin{align}
\dot{\rho}+3\frac{\dot{a}}{a}\left(\rho+\frac{P}{c^2}\right)=0;\\
\frac{d\rho}{\rho}=-3\frac{da}{a}(1+w).
\end{align}</math>

If {{mvar|w}} is constant, then

<math display="block">\ln{\rho}=-3(1+w)\ln{a};</math>

implying:

<math display="block">\rho=a^{-3(1+w)}.</math>

Therefore, for dark energy with a constant equation of state {{mvar|w}}, {{nowrap|<math>\rho_{de}(a)= \rho_{de0}a^{-3(1+w)}</math>.}} If this is substituted into the Friedman equation in a similar way as before, but this time set {{math|1= ''k'' = 0}}, which assumes a spatially flat universe, then (see [[shape of the universe]])

<math display="block">H^2(z)= H_0^2 \left( \Omega_m (1+z)^{3} + \Omega_{de}(1+z)^{3(1+w)} \right).</math>

If the dark energy derives from a cosmological constant such as that introduced by Einstein, it can be shown that {{math|1= ''w'' = −1}}. The equation then reduces to the last equation in the matter-dominated universe section, with {{math|Ω{{sub|''k''}}}} set to zero. In that case the initial dark energy density {{math|''ρ''{{sub|''de''0}}}} is given by<ref>{{cite book|last1=Carroll|first1=Sean|title=Spacetime and Geometry: An Introduction to General Relativity|edition=illustrated|date=2004|publisher=Addison-Wesley|location=San Francisco|isbn=978-0-8053-8732-2|page=328|url=https://books.google.com/books?id=1SKFQgAACAAJ}}</ref>

<math display="block">\begin{align}
\rho_{de0} &= \frac{\Lambda c^2}{8 \pi G} \,, \\
\Omega_{de} &=\Omega_{\Lambda}.
\end{align}</math>

If dark energy does not have a constant equation-of-state {{mvar|w}}, then

<math display="block">\rho_{de}(a)= \rho_{de0}e^{-3\int\frac{da}{a}\left(1+w(a)\right)},</math>

and to solve this, {{math|''w''(''a'')}} must be parametrized, for example if {{math|1= ''w''(''a'') = ''w''{{sub|0}} + ''w''{{sub|''a''}}(1−''a'')}}, giving<ref>{{cite journal |last1=Heneka |first1=C. |last2=Amendola |first2=L. |date=2018 |title=General modified gravity with 21cm intensity mapping: simulations and forecast |journal=[[Journal of Cosmology and Astroparticle Physics]] |volume=2018 |issue=10 |page=004 |doi=10.1088/1475-7516/2018/10/004 |arxiv=1805.03629 |bibcode=2018JCAP...10..004H |s2cid=119224326 }}</ref>

<math display="block">H^2(z)= H_0^2 \left( \Omega_m a^{-3} + \Omega_{de}a^{-3\left(1+w_0 +w_a \right)}e^{-3w_a(1-a)} \right).</math>

== Units derived from the Hubble constant ==
=== Hubble time ===
The Hubble constant {{math|''H''{{sub|0}}}} has units of inverse time; the '''Hubble time''' {{mvar|t{{sub|H}}}} is simply defined as the inverse of the Hubble constant,<ref>{{cite book |last1=Hawley |first1=John F. |title=Foundations of modern cosmology |last2=Holcomb |first2=Katherine A. |date=2005 |publisher=Oxford University Press |isbn=978-0-19-853096-1 |edition=2nd |location=Oxford [u.a.] |pages=304 |language=en-uk}}</ref> i.e.

<math display="block">t_H \equiv \frac{1}{H_0} = \frac{1}{67.8 \mathrm{~(km/s)/Mpc}} = 4.55\times 10^{17} \mathrm{~s} = 14.4 \text{ billion years}.</math>

This is slightly different from the [[age of the universe]], which is approximately 13.8&nbsp;billion years. The Hubble time is the age it would have had if the expansion had been linear,<ref>{{Cite book |last=Ridpath |first=Ian |title=A Dictionary of Astronomy |publisher=Oxford University Press |year=2012 |isbn=9780199609055 |edition=2nd |page=225 |language=en |doi=10.1093/acref/9780199609055.001.0001}}</ref> and it is different from the real age of the universe because the expansion is not linear; it depends on the energy content of the universe (see {{slink||Derivation of the Hubble parameter}}).

We currently appear to be approaching a period where the expansion of the universe is exponential due to the increasing dominance of [[vacuum energy]]. In this regime, the Hubble parameter is constant, and the universe grows by a factor [[E (mathematical constant)|{{mvar|e}}]] each Hubble time:

<math display="block">H \equiv \frac{\dot a}{a} = \textrm{constant} \quad \Longrightarrow \quad a \propto e^{Ht} = e^{\frac{t}{t_H}}</math>

Likewise, the generally accepted value of 2.27&nbsp;[[Exa-|Es]]<sup>−1</sup> means that (at the current rate) the universe would grow by a factor of {{mvar|e}}{{sup|2.27}} in one [[exasecond]].

Over long periods of time, the dynamics are complicated by general relativity, dark energy, [[Inflation (cosmology)|inflation]], etc., as explained above.

=== Hubble length ===
The Hubble length or Hubble distance is a unit of distance in cosmology, defined as {{math|''cH''{{sup|−1}}}} — the speed of light multiplied by the Hubble time. It is equivalent to 4,420 million parsecs or 14.4 billion light years. (The numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years.) Substituting {{math|1= ''D'' = ''cH''{{sup|−1}}}} into the equation for Hubble's law, {{math|''v'' {{=}} ''H''<sub>0</sub>''D''}} reveals that the Hubble distance specifies the distance from our location to those galaxies which are {{em|currently}} receding from us at the speed of light.

=== Hubble volume ===
{{main|Hubble volume}}
The Hubble volume is sometimes defined as a volume of the universe with a [[Comoving and proper distances|comoving]] size of {{math|''cH''{{sup|−1}}}}. The exact definition varies: it is sometimes defined as the volume of a sphere with radius {{math|''cH''{{sup|−1}}}}, or alternatively, a cube of side {{math|''cH''{{sup|−1}}}}. Some cosmologists even use the term Hubble volume to refer to the volume of the [[observable universe]], although this has a radius approximately three times larger.

== Determining the Hubble constant ==
[[File:Recent Hubble's Constant Values.png|thumb|The value of the Hubble constant in (km/s)/Mpc, including measurement uncertainty, for recent surveys<ref name="planck_overview"/>]]
The value of the Hubble constant, {{math|''H''{{sub|0}}}}, cannot be measured directly, but is derived from a combination of astronomical observations and model-dependent assumptions. Increasingly accurate observations and new models over many decades have led to two sets of highly precise values which do not agree. This difference is known as the "Hubble tension".<ref name="NYT-20170220" /><ref name=VerdeReview2024/>

=== Earlier measurements ===
For the original 1929 estimate of the constant now bearing his name, Hubble used observations of [[Cepheid variable]] stars as "[[Cosmic distance ladder#Standard_candles|standard candles]]" to measure distance.<ref name=Allen/> The result he obtained was {{val|500|u=km/s|up=Mpc}}, much larger than the value astronomers currently calculate. Later observations by astronomer [[Walter Baade]] led him to realize that there were distinct "[[stellar population|populations]]" for stars (Population I and Population II) in a galaxy. The same observations led him to discover that there are two types of Cepheid variable stars with different luminosities. Using this discovery, he recalculated Hubble constant and the size of the known universe, doubling the previous calculation made by Hubble in 1929.<ref>Baade, W. (1944) The resolution of Messier 32, NGC 205, and the central region of the Andromeda nebula. ApJ 100 137–146</ref><ref>Baade, W. (1956) The period-luminosity relation of the Cepheids. PASP 68 5–16</ref><ref name=Allen>{{cite web|last=Allen|first=Nick|title=Section 2: The Great Debate and the Great Mistake: Shapley, Hubble, Baade|url=http://www.institute-of-brilliant-failures.com/section2.htm|website=The Cepheid Distance Scale: A History|access-date=19 November 2011|archive-url=https://web.archive.org/web/20071210105344/http://www.institute-of-brilliant-failures.com/section2.htm|archive-date=10 December 2007|url-status=dead}}</ref> He announced this finding to considerable astonishment at the 1952 meeting of the [[International Astronomical Union]] in Rome.

For most of the second half of the 20th century, the value of {{math|''H''{{sub|0}}}} was estimated to be between {{val|50|and|90|u=km/s|up=Mpc}}.

The value of the Hubble constant was the topic of a long and rather bitter controversy between [[Gérard de Vaucouleurs]], who claimed the value was around 100, and [[Allan Sandage]], who claimed the value was near 50.<ref name="Overbye"/> In one demonstration of vitriol shared between the parties, when Sandage and [[Gustav Andreas Tammann]] (Sandage's research colleague) formally acknowledged the shortcomings of confirming the systematic error of their method in 1975, Vaucouleurs responded "It is unfortunate that this sober warning was so soon forgotten and ignored by most astronomers and textbook writers".<ref name=":0">{{Cite book |last=de Vaucouleurs |first=G. |title=The cosmic distance scale and the Hubble constant |publisher=Mount Stromlo and Siding Spring Observatories, Australian National University |year=1982}}</ref> In 1996, a debate moderated by [[John N. Bahcall|John Bahcall]] between Sidney van den Bergh and Gustav Tammann was held in similar fashion to the earlier Shapley–Curtis debate over these two competing values.

This previously wide variance in estimates was partially resolved with the introduction of the [[Lambda-CDM model|ΛCDM]] model of the universe in the late 1990s. Incorporating the ΛCDM model, observations of high-redshift clusters at X-ray and microwave wavelengths using the [[Sunyaev–Zel'dovich effect]], measurements of anisotropies in the [[cosmic microwave background]] radiation, and optical surveys all gave a value of around 50–70&nbsp;km/s/Mpc for the constant.<ref name=Myers1999>{{cite journal |title=Scaling the universe: Gravitational lenses and the Hubble constant |last=Myers |first=S. T. |date=1999 |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=96 |issue=8 |pages=4236–4239 |doi=10.1073/pnas.96.8.4236 |doi-access=free |pmid=10200245 |pmc=33560|bibcode=1999PNAS...96.4236M }}</ref>

=== Precision cosmology and the Hubble tension {{anchor|Hubble tension}} <!-- Hubble tension redirect here -->===
By the late 1990s, advances in ideas and technology allowed higher precision measurements.<ref name=Turner-2022>{{Cite journal |last=Turner |first=Michael S. |date=2022-09-26 |title=The Road to Precision Cosmology |url=https://www.annualreviews.org/content/journals/10.1146/annurev-nucl-111119-041046 |journal=Annual Review of Nuclear and Particle Science |language=en |volume=72 |pages=1–35 |doi=10.1146/annurev-nucl-111119-041046 |arxiv=2201.04741 |bibcode=2022ARNPS..72....1T |issn=0163-8998}}</ref>
However, two major categories of methods, each with high precision, fail to agree.
"Late universe" measurements using calibrated distance ladder techniques have converged on a value of approximately {{val|73|u=km/s|up=Mpc}}. Since 2000, "early universe" techniques based on measurements of the [[cosmic microwave background]] have become available, and these agree on a value near {{val|67.7|u=km/s|up=Mpc}}.<ref>{{Cite journal |last1=Freedman |first1=Wendy L. |last2=Madore |first2=Barry F. |date=2023-11-01 |title=Progress in direct measurements of the Hubble constant |url=https://doi.org/10.1088/1475-7516/2023/11/050 |journal=Journal of Cosmology and Astroparticle Physics |volume=2023 |issue=11 |article-number=050 |doi=10.1088/1475-7516/2023/11/050 |issn=1475-7516|arxiv=2309.05618 |bibcode=2023JCAP...11..050F }}</ref> (This accounts for the change in the expansion rate since the early universe, so is comparable to the first number.) Initially, this discrepancy was within the estimated [[Measurement uncertainty|measurement uncertainties]] and thus no cause for concern.  However, as techniques have improved, the estimated measurement uncertainties have shrunk, but the discrepancies have ''not'', to the point that the disagreement is now highly [[statistically significant]]. This discrepancy is called the '''Hubble tension'''.<ref name="LS-20190826">{{cite news |last=Mann |first=Adam |date=26 August 2019 |title=One Number Shows Something Is Fundamentally Wrong with Our Conception of the Universe – This fight has universal implications |work=[[Live Science]] |url=https://www.livescience.com/hubble-constant-discrepancy-explained.html |access-date=26 August 2019}}</ref><ref name="di Valentino 2021 153001">{{cite journal |last=di Valentino |first=Eleonora |display-authors=etal |date=2021 |title=In the realm of the Hubble tension—a review of solutions |journal=Classical and Quantum Gravity |volume=38 |issue=15 |article-number=153001 |doi=10.1088/1361-6382/ac086d |doi-access=free |arxiv=2103.01183 |bibcode=2021CQGra..38o3001D |s2cid=232092525}}</ref>

An example of an "early" measurement, the [[Planck (spacecraft)|Planck mission]] published in 2018 gives a value for {{math|1= ''H''{{sub|0}} =}} of {{val|67.4|0.5|u=km/s|up=Mpc}}.<ref name="2018planckcosmos"/> In the "late" camp is the higher value of {{val|74.03|1.42|u=km/s|up=Mpc}} determined by the  [[Hubble Space Telescope]]<ref name="SA2019">{{Cite magazine|url=https://www.scientificamerican.com/article/best-yet-measurements-deepen-cosmological-crisis/|title=Best-Yet Measurements Deepen Cosmological Crisis|last=Ananthaswamy|first=Anil|date=22 March 2019|access-date=23 March 2019|magazine=Scientific American}}</ref> 
and confirmed by the [[James Webb Space Telescope]] in 2023.<ref>{{Citation |last1=Riess |first1=Adam G. |title=Crowded No More: The Accuracy of the Hubble Constant Tested with High Resolution Observations of Cepheids by JWST |date=2023-07-28 |arxiv=2307.15806 |last2=Anand |first2=Gagandeep S. |last3=Yuan |first3=Wenlong |last4=Casertano |first4=Stefano |last5=Dolphin |first5=Andrew |last6=Macri |first6=Lucas M. |last7=Breuval |first7=Louise |last8=Scolnic |first8=Dan |last9=Perrin |first9=Marshall |journal=The Astrophysical Journal |volume=956 |issue=1 |article-number=L18 |doi=10.3847/2041-8213/acf769 |doi-access=free |bibcode=2023ApJ...956L..18R }}</ref><ref>{{Cite web |date=2023-09-12 |title=Webb Confirms Accuracy of Universe's Expansion Rate Measured by Hubble, Deepens Mystery of Hubble Constant Tension – James Webb Space Telescope |url=https://blogs.nasa.gov/webb/2023/09/12/webb-confirms-accuracy-of-universes-expansion-rate-measured-by-hubble-deepens-mystery-of-hubble-constant-tension/ |access-date=2024-02-15 |website=blogs.nasa.gov |language=en-US}}</ref>
The "early" and "late" measurements disagree at the >5 [[Standard deviation|''σ'']] level, beyond a plausible level of chance.<ref name="Riess2019"/><ref>{{Cite journal |last1=Riess |first1=Adam G. |last2=Yuan |first2=Wenlong |last3=Macri |first3=Lucas M. |last4=Scolnic |first4=Dan |last5=Brout |first5=Dillon |last6=Casertano |first6=Stefano |last7=Jones |first7=David O. |last8=Murakami |first8=Yukei |last9=Anand |first9=Gagandeep S. |last10=Breuval |first10=Louise |last11=Brink |first11=Thomas G. |last12=Filippenko |first12=Alexei V. |last13=Hoffmann |first13=Samantha |last14=Jha |first14=Saurabh W. |last15=Kenworthy |first15=W. D’arcy |date=July 2022 |title=A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team |journal=The Astrophysical Journal Letters |language=en |volume=934 |issue=1 |pages=L7 |doi=10.3847/2041-8213/ac5c5b |doi-access=free |bibcode=2022ApJ...934L...7R |issn=2041-8205|arxiv=2112.04510 }}</ref> The resolution to this disagreement is an ongoing area of active research.<ref>{{Cite journal|last1=Millea|first1=Marius|last2=Knox|first2=Lloyd|date=2019-08-10|title=Hubble constant hunter's guide|journal=Physical Review D |volume=101 |issue=4 |page=043533 |doi=10.1103/PhysRevD.101.043533 |language=en|arxiv=1908.03663}}</ref> 

[[File:Measurements of the Hubble constant (H0) by different astronomical missions and groups until 2021.jpg|thumb|upright=2.3|The landscape of H0 measurements around 2021, with the 2018 results from CMB measurements highlighted in pink and 2020 distance ladder values highlighted in cyan.<ref name="di Valentino 2021 153001" />]]

=== Reducing systematic errors ===
Since 2013 much effort has gone in to new measurements to check for possible systematic errors and improved reproducibility.<ref name=VerdeReview2024/>

The "late universe" or distance ladder measurements typically employ three stages or "rungs". In the first rung distances to [[Cepheids]] are determined while trying to reduce luminosity errors from dust and correlations of [[metallicity]] with luminosity. The second rung uses 
[[Type Ia supernova]], explosions of almost constant amount of mass and thus very similar amounts of light; the primary source of systematic error is the limited number of objects that can be observed. The third rung of the distance ladder measures the red-shift of supernova to extract the Hubble flow and from that the constant. At this rung corrections due to [[peculiar velocity|motion other than expansion]] are applied.<ref name=VerdeReview2024/>{{rp|2.1}} 
As an example of the kind of work needed to reduce systematic errors, photometry on observations from the James Webb Space Telescope of extra-galactic Cepheids confirm the findings from the HST. The higher resolution avoided confusion from crowding of stars in the field of view but came to the same value for H<sub>0</sub>.<ref>{{Cite journal |last1=Riess |first1=Adam G. |last2=Anand |first2=Gagandeep S. |last3=Yuan |first3=Wenlong |last4=Casertano |first4=Stefano |last5=Dolphin |first5=Andrew |last6=Macri |first6=Lucas M. |last7=Breuval |first7=Louise |last8=Scolnic |first8=Dan |last9=Perrin |first9=Marshall |last10=Anderson |first10=Richard I. |date=2023-10-01 |title=Crowded No More: The Accuracy of the Hubble Constant Tested with High-resolution Observations of Cepheids by JWST |journal=The Astrophysical Journal Letters |volume=956 |issue=1 |pages=L18 |doi=10.3847/2041-8213/acf769 |doi-access=free |issn=2041-8205|arxiv=2307.15806 |bibcode=2023ApJ...956L..18R }}</ref><ref name=VerdeReview2024>{{Cite journal |last1=Verde |first1=Licia |last2=Schöneberg |first2=Nils |last3=Gil-Marín |first3=Héctor |date=2024-09-13 |title=A Tale of Many H0 |url=https://www.annualreviews.org/content/journals/10.1146/annurev-astro-052622-033813 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=62 |pages=287–331 |doi=10.1146/annurev-astro-052622-033813 |issn=0066-4146}}</ref>

The "early universe" or inverse distance ladder measures the observable consequences of spherical sound waves on primordial plasma density. These pressure waves – called [[baryon acoustic oscillations]] (BAO) – cease once the universe cooled enough for electrons to stay bound to nuclei, ending the plasma and allowing the photons trapped by interaction with the plasma to escape. The pressure waves then become very small perturbations in density imprinted on the cosmic microwave background and on the large scale density of galaxies across the sky. Detailed structure in high precision measurements of the CMB can be matched to physics models of the oscillations. These models depend upon the Hubble constant such that a match reveals a value for the constant. Similarly, the BAO affects the statistical distribution of matter, observed as distant galaxies across the sky. These two independent kinds of measurements produce similar values for the constant from the current models, giving strong evidence that systematic errors in the measurements themselves do not affect the result.<ref name=VerdeReview2024/>{{rp|Sup. B}}

=== Other kinds of measurements ===
In addition to measurements based on calibrated distance ladder techniques or measurements of the CMB, other methods have been used to determine the Hubble constant.

One alternative method for constraining the Hubble constant involves transient events seen in multiple images of a [[strong gravitational lensing|strongly lensed]] object. A transient event, such as a supernova, is seen at different times in each of the lensed images, and if this ''time delay'' between each image can be measured, it can be used to constrain the Hubble constant. This method is commonly known as "time-delay cosmography", and was first proposed by [[Sjur Refsdal|Refsdal]] in 1964,<ref>{{cite journal |last1=Refsdal |first1=S. |title=On the Possibility of Determining Hubble's Parameter and the Masses of Galaxies from the Gravitational Lens Effect |journal=Monthly Notices of the Royal Astronomical Society |date=1 September 1964 |volume=128 |issue=4 |pages=307–310 |doi=10.1093/mnras/128.4.307|doi-access=free }}</ref> years before the first strongly lensed object was observed. The first strongly lensed supernova to be discovered was named [[SN Refsdal]] in his honor. While Refsdal suggested this could be done with supernovae, he also noted that extremely luminous and distant star-like objects could also be used. These objects were later named [[quasar|quasars]], and to date (April 2025) the majority of time-delay cosmography measurements have been done with strongly lensed quasars. This is because current samples of lensed quasars vastly outnumber known lensed supernovae, of which <10 are known. This is expected to change dramatically in the next few years, with surveys such as [[Vera C. Rubin Observatory|LSST]] expected to discover ~10 lensed SNe in the first three years of observation.<ref>{{cite arXiv|eprint=2504.01068 |last1=Bronikowski |first1=M. |last2=Petrushevska |first2=T. |last3=Pierel |first3=J. D. R. |last4=Acebron |first4=A. |last5=Donevski |first5=D. |last6=Apostolova |first6=B. |last7=Blagorodnova |first7=N. |last8=Jankovič |first8=T. |title=Cluster-lensed supernova yields from the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope |date=2025 |class=astro-ph.GA }}</ref> For example time-delay constraints on H0, see the results from STRIDES and H0LiCOW in the table below.

In October 2018, scientists used information from [[gravitational wave]] events (especially those involving the [[Neutron star merger|merger of neutron stars]], like [[GW170817]]), of determining the Hubble constant.<ref name="PHYS-20181022">{{cite web |last=Lerner |first=Louise |title=Gravitational waves could soon provide measure of universe's expansion |url=https://phys.org/news/2018-10-gravitational-universe-expansion.html |date=22 October 2018 |work=[[Phys.org]] |access-date=22 October 2018 }}</ref><ref name="NAT-20181017">{{cite journal |last1=Chen |first1=Hsin-Yu |last2=Fishbach |first2=Maya |last3=Holz |first3=Daniel E. |title=A two per cent Hubble constant measurement from standard sirens within five years |date=17 October 2018 |journal=[[Nature (journal)|Nature]] |volume=562 |issue=7728 |pages=545–547 |doi=10.1038/s41586-018-0606-0 |pmid=30333628 |bibcode=2018Natur.562..545C |arxiv=1712.06531 |s2cid=52987203 }}</ref>

In July 2019, astronomers reported that a new method to determine the Hubble constant, and resolve the discrepancy of earlier methods, has been proposed based on the mergers of pairs of [[neutron star]]s, following the detection of the neutron star merger of GW170817, an event known as a [[dark siren]].<ref name="EA-20190708">{{cite news |author=National Radio Astronomy Observatory |author-link=National Radio Astronomy Observatory |date=8 July 2019 |title=New method may resolve difficulty in measuring universe's expansion – Neutron star mergers can provide new 'cosmic ruler' |work=[[EurekAlert!]] |url=https://www.eurekalert.org/pub_releases/2019-07/nrao-nmm070819.php |access-date=8 July 2019}}</ref><ref name="NRAO-20190708">{{cite news |last=Finley |first=Dave |title=New Method May Resolve Difficulty in Measuring Universe's Expansion |url=https://public.nrao.edu/news/new-method-measuring-universe-expansion/ |date=8 July 2019 |work=[[National Radio Astronomy Observatory]] |access-date=8 July 2019 }}</ref> Their measurement of the Hubble constant is {{val|73.3|+5.3|-5.0}} (km/s)/Mpc.<ref name="NAT-20190708">{{cite journal |author=Hotokezaka, K. |display-authors=et al. |title=A Hubble constant measurement from superluminal motion of the jet in GW170817 |date=8 July 2019 |journal=[[Nature Astronomy]] |volume=3 |issue=10 |pages=940–944 |doi=10.1038/s41550-019-0820-1 |bibcode=2019NatAs...3..940H |arxiv=1806.10596 |s2cid=119547153 }}</ref> 

Also in July 2019, astronomers reported another new method, using data from the [[Hubble Space Telescope]] and based on distances to [[Red giant|red giant stars]] calculated using the [[tip of the red-giant branch]] (TRGB) distance indicator. Their measurement of the Hubble constant is {{val|69.8|+1.9|-1.9|u=km/s|up=Mpc}}.<ref name="EA-20190716" /><ref name="SCI-20190719" /><ref name="The Carnegie-Chicago Hubble Program">{{cite journal |last1=Freedman |first1=Wendy L. |author-link1=Wendy Freedman |last2=Madore |first2=Barry F. |last3=Hatt |first3=Dylan |last4=Hoyt |first4=Taylor J. |last5=Jang |first5=In-Sung |last6=Beaton |first6=Rachael L. |last7=Burns |first7=Christopher R. |last8=Lee |first8=Myung Gyoon |last9=Monson |first9=Andrew J. |last10=Neeley |first10=Jillian R. |last11=Phillips |first11=Mark M. |last12=Rich |first12=Jeffrey A. |last13=Seibert |first13=Mark |display-authors=6 |year=2019 |title=The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch |journal=The Astrophysical Journal |volume=882 |issue=1 |article-number=34 |arxiv=1907.05922 |bibcode=2019ApJ...882...34F |doi=10.3847/1538-4357/ab2f73 |s2cid=196623652 |doi-access=free }}</ref> 

In February 2020, the Megamaser Cosmology Project published independent results based on [[astrophysical masers]] visible at cosmological distances and which do not require multi-step calibration.  That work confirmed the distance ladder results and differed from the early-universe results at a statistical significance level of 95%.<ref name="megamaser" /> 

In July 2020, measurements of the cosmic background radiation by the [[Atacama Cosmology Telescope]] predict that the Universe should be expanding more slowly than is currently observed.<ref>{{Cite journal|last=Castelvecchi|first=Davide|date=2020-07-15|title=Mystery over Universe's expansion deepens with fresh data|journal=Nature|language=en|volume=583|issue=7817|pages=500–501|doi=10.1038/d41586-020-02126-6|pmid=32669728|bibcode=2020Natur.583..500C|s2cid=220583383|doi-access=}}</ref>

In July 2023, an independent estimate of the Hubble constant was derived from a [[kilonova]], the optical afterglow of a [[neutron star merger]], using the [[expanding photosphere method]].<ref name="aanda.org">{{Cite journal |last1=Sneppen |first1=Albert |last2=Watson |first2=Darach |last3=Poznanski |first3=Dovi |last4=Just |first4=Oliver |last5=Bauswein |first5=Andreas |last6=Wojtak |first6=Radosław |date=2023-10-01 |title=Measuring the Hubble constant with kilonovae using the expanding photosphere method |url=https://www.aanda.org/articles/aa/abs/2023/10/aa46306-23/aa46306-23.html |journal=Astronomy & Astrophysics |language=en |volume=678 |article-number=A14 |doi=10.1051/0004-6361/202346306 |issn=0004-6361|arxiv=2306.12468 |bibcode=2023A&A...678A..14S }}</ref> Due to the blackbody nature of early kilonova spectra,<ref>{{Cite journal |last=Sneppen |first=Albert |date=2023-09-01 |title=On the Blackbody Spectrum of Kilonovae |journal=The Astrophysical Journal |volume=955 |issue=1 |article-number=44 |doi=10.3847/1538-4357/acf200 |doi-access=free |issn=0004-637X|arxiv=2306.05452 |bibcode=2023ApJ...955...44S }}</ref> such systems provide strongly constraining estimators of cosmic distance. Using the kilonova [[AT2017gfo]] (the aftermath of, once again, GW170817), these measurements indicate a local-estimate of the Hubble constant of {{val|67.0|+3.6|u=km/s|up=Mpc}}.<ref name="nature.com">{{Cite journal |last1=Sneppen |first1=Albert |last2=Watson |first2=Darach |last3=Bauswein |first3=Andreas |last4=Just |first4=Oliver |last5=Kotak |first5=Rubina |last6=Nakar |first6=Ehud |last7=Poznanski |first7=Dovi |last8=Sim |first8=Stuart |date=February 2023 |title=Spherical symmetry in the kilonova AT2017gfo/GW170817 |url=https://www.nature.com/articles/s41586-022-05616-x |journal=Nature |language=en |volume=614 |issue=7948 |pages=436–439 |doi=10.1038/s41586-022-05616-x |pmid=36792736 |arxiv=2302.06621 |bibcode=2023Natur.614..436S |s2cid=256846834 |issn=1476-4687}}</ref><ref name="aanda.org"/>
[[File:Hubbleconstants color.png|centre|upright=3.8|thumb|Estimated values of the Hubble constant, 2001–2020. Estimates in black represent calibrated distance ladder measurements which tend to cluster around {{val|73||u=km/s|up=Mpc}}; red represents early universe CMB/BAO measurements with ΛCDM parameters which show good agreement on a figure near {{val|67|u=km/s|up=Mpc}}, while blue are other techniques, whose uncertainties are not yet small enough to decide between the two.]]

=== Possible resolutions of the Hubble tension ===
The cause of the Hubble tension is unknown,<ref>{{cite web |last1=Gresko |first1=Michael |title=The universe is expanding faster than it should be |url=https://www.nationalgeographic.com/science/article/the-universe-is-expanding-faster-than-it-should-be |archive-url=https://web.archive.org/web/20211217160427/https://www.nationalgeographic.com/science/article/the-universe-is-expanding-faster-than-it-should-be |url-status=dead |archive-date=December 17, 2021 |date=17 December 2021 |website=[[National Geographic]] |access-date=21 December 2021}}</ref> and there are many possible proposed solutions. The most conservative is that there is an unknown systematic error affecting either early-universe or late-universe observations. Although intuitively appealing, this explanation requires multiple unrelated effects regardless of whether early-universe or late-universe observations are incorrect, and there are no obvious candidates. Furthermore, any such systematic error would need to affect multiple different instruments, since both the early-universe and late-universe observations come from several different telescopes.<ref name=VerdeReview2024/>

Alternatively, it could be that the observations are correct, but some unaccounted-for effect is causing the discrepancy. If the [[cosmological principle]] fails (see {{slink|Lambda-CDM model|Violations of the cosmological principle}}), then the existing interpretations of the Hubble constant and the Hubble tension have to be revised, which might resolve the Hubble tension.<ref name="Snowmass21">{{citation |last1=Abdalla |first1=Elcio |title=Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies |date=11 Mar 2022 |journal=Journal of High Energy Astrophysics |volume=34 |page=49 |arxiv=2203.06142 |bibcode=2022JHEAp..34...49A |doi=10.1016/j.jheap.2022.04.002 |s2cid=247411131 |last2=Abellán |first2=Guillermo Franco |last3=Aboubrahim |first3=Amin}}</ref> In particular, we would need to be located within a very large void, up to about a redshift of 0.5, for such an explanation to conflate with supernovae and [[baryon acoustic oscillation]] observations.<ref name="di Valentino 2021 153001" /> Yet another possibility is that the uncertainties in the measurements could have been underestimated, but given the internal agreements this is neither likely, nor resolves the overall tension.<ref name=VerdeReview2024/>

Finally, another possibility is new physics beyond the currently accepted cosmological model of the universe, the [[Lambda-CDM model|ΛCDM model]].<ref name="di Valentino 2021 153001"/><ref>{{Cite journal |last=Vagnozzi |first=Sunny |date=2020-07-10 |title=New physics in light of the ''H''<sub>0</sub> tension: An alternative view |url=https://link.aps.org/doi/10.1103/PhysRevD.102.023518 |journal=Physical Review D |volume=102 |issue=2 |article-number=023518 |doi=10.1103/PhysRevD.102.023518|arxiv=1907.07569 |bibcode=2020PhRvD.102b3518V |s2cid=197430820 }}</ref> There are very many theories in this category, for example, replacing general relativity with [[modified Newtonian dynamics|a modified theory of gravity]] could potentially resolve the tension,<ref name="Haslbauer">{{Cite journal |last1=Haslbauer |first1=M. |last2=Banik |first2=I. |last3=Kroupa |first3=P. |date=2020-12-21 |title=The KBC void and Hubble tension contradict LCDM on a Gpc scale – Milgromian dynamics as a possible solution |journal=Monthly Notices of the Royal Astronomical Society |volume=499 |issue=2 |pages=2845–2883 |arxiv=2009.11292 |bibcode=2020MNRAS.499.2845H |doi=10.1093/mnras/staa2348 |issn=0035-8711 |doi-access=free}}</ref><ref name="Mazurenko">{{Cite journal |last1=Mazurenko |first1=S. |last2=Banik |first2=I. |last3=Kroupa |first3=P. |last4=Haslbauer |first4=M. |date=2024-01-21 |title=A simultaneous solution to the Hubble tension and observed bulk flow within 250/h Mpc |journal=Monthly Notices of the Royal Astronomical Society |volume=527 |issue=3 |pages=4388–4396 |arxiv=2311.17988 |bibcode=2024MNRAS.527.4388M |doi=10.1093/mnras/stad3357 |issn=0035-8711 |doi-access=free}}</ref> as can a dark energy component in the early universe,{{efn|In standard ΛCDM, dark energy only comes into play in the late universe – its effect in the early universe is too small to have an effect.}}<ref>{{Cite journal |last1=Poulin|first1=Vivian |last2=Smith|first2=Tristan L. |last3=Karwal|first3=Tanvi |last4=Kamionkowski|first4=Marc |date=2019-06-04 |title=Early Dark Energy can Resolve the Hubble Tension |journal=Physical Review Letters |volume=122 |issue=22 |article-number=221301 |doi=10.1103/PhysRevLett.122.221301 |pmid=31283280 |arxiv=1811.04083 |bibcode=2019PhRvL.122v1301P |s2cid=119233243 }}</ref> dark energy with a time-varying [[Equation of state (cosmology)|equation of state]],{{efn|1=In standard ΛCDM, dark energy has a constant equation of state {{math|1= ''w'' = −1}}.}}<ref>{{cite journal|url=https://www.nature.com/articles/s41550-017-0216-z|title=Dynamical dark energy in light of the latest observations|journal=Nature Astronomy|date=2017|doi=10.1038/s41550-017-0216-z |last1=Zhao |first1=Gong-Bo |last2=Raveri |first2=Marco |last3=Pogosian |first3=Levon |last4=Wang |first4=Yuting |last5=Crittenden |first5=Robert G. |last6=Handley |first6=Will J. |last7=Percival |first7=Will J. |last8=Beutler |first8=Florian |last9=Brinkmann |first9=Jonathan |last10=Chuang |first10=Chia-Hsun |last11=Cuesta |first11=Antonio J. |last12=Eisenstein |first12=Daniel J. |last13=Kitaura |first13=Francisco-Shu |last14=Koyama |first14=Kazuya |last15=l'Huillier |first15=Benjamin |last16=Nichol |first16=Robert C. |last17=Pieri |first17=Matthew M. |last18=Rodriguez-Torres |first18=Sergio |last19=Ross |first19=Ashley J. |last20=Rossi |first20=Graziano |last21=Sánchez |first21=Ariel G. |last22=Shafieloo |first22=Arman |last23=Tinker |first23=Jeremy L. |last24=Tojeiro |first24=Rita |last25=Vazquez |first25=Jose A. |last26=Zhang |first26=Hanyu |volume=1 |issue=9 |pages=627–632 |arxiv=1701.08165 |bibcode=2017NatAs...1..627Z |s2cid=256705070 }}</ref> or [[dark matter]] that decays into dark radiation.<ref>{{cite journal|url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.92.061303|title=Reconciling Planck results with low redshift astronomical measurements|journal=Physical Review D|date=2015|doi=10.1103/PhysRevD.92.061303 |last1=Berezhiani |first1=Zurab |last2=Dolgov |first2=A. D. |last3=Tkachev |first3=I. I. |volume=92 |issue=6 |article-number=061303 |arxiv=1505.03644 |bibcode=2015PhRvD..92f1303B |s2cid=118169478 }}</ref> A problem faced by all these theories is that both early-universe and late-universe measurements rely on multiple independent lines of physics, and it is difficult to modify any of those lines while preserving their successes elsewhere. The scale of the challenge can be seen from how some authors have argued that new early-universe physics alone is not sufficient;<ref>{{cite web|url=https://astrobites.org/2021/05/17/template-post-5/|title=Solving the Hubble tension might require more than changing the early Universe|author=Laila Linke|publisher=Astrobites|date=17 May 2021}}</ref><ref>{{Cite journal |last1=Vagnozzi|first1=Sunny |date=2023-08-30 |title=Seven Hints That Early-Time New Physics Alone Is Not Sufficient to Solve the Hubble Tension |journal=Universe |volume=9 |issue=9 |article-number=393 |doi=10.3390/universe9090393 |arxiv=2308.16628 |bibcode=2023Univ....9..393V |doi-access=free }} </ref> while other authors argue that new late-universe physics alone is also not sufficient.<ref>{{cite journal|title=Ruling Out New Physics at Low Redshift as a Solution to the H<sub>0</sub> Tension|author=Ryan E. Keeley and Arman Shafieloo|journal=Physical Review Letters |date=August 2023|volume=131 |issue=11 |article-number=111002 |doi=10.1103/PhysRevLett.131.111002 |pmid=37774270 |arxiv=2206.08440 |bibcode=2023PhRvL.131k1002K |s2cid=249848075 }}</ref> Nonetheless, astronomers are trying, with interest in the Hubble tension growing strongly since the mid 2010s.<ref name="di Valentino 2021 153001" />

== Measurements of the Hubble constant ==
{| class="wikitable sortable" style="width:100%; font-size:96%;"
|-
! Date published
! Hubble constant <br /> (km/s)/Mpc
! Observer
! class="unsortable"| Citation
! class="unsortable" | Remarks / methodology
<!-- Add entries in reverse chronological order (newest at the top). Do not remove older entries unless retracted by publisher. Add notes in remarks column as needed. -->
|-
|2025-01-14
|{{val|75.7|+8.1|-5.5}}
|Pascale et al.
|<ref>{{Cite journal |last1=Pascale |first1=Massimo |last2=Frye |first2=Brenda L. |last3=Pierel |first3=Justin D.R. |last4=Chen |first4=Wenlei |last5=Kelly |first5=Patrick L. |last6=Cohen |first6=Seth H. |last7=Windhorst |first7=Rogier A. |last8=Riess |first8=Adam G. |last9=Kamieneski |first9=Patrick S. |last10=Diego |first10=Jos’e M. |last11=Meena |first11=Ashish K. |last12=Cha |first12=Sangjun |last13=Oguri |first13=Masamune |last14=Zitrin |first14=Adi |last15=Jee |first15=M. James |date=2025-01-14 |title=SN H0pe: The First Measurement of H<sub>0</sub> from a Multiply Imaged Type Ia Supernova, Discovered by JWST |journal=The Astrophysical Journal |language=en |volume=979 |issue=1 |pages=13 |doi=10.3847/1538-4357/ad9928 |doi-access=free |arxiv=2403.18902 |bibcode=2025ApJ...979...13P |issn=0004-637X}}</ref>
|Timing delay of gravitationally lensed images of [[SN Refsdal#Other multiply-lensed supernova|Supernova H0pe]]. Independent of cosmic distance ladder or the CMB. JWST data. (Same method as 2023-05-11 cell.)
|-
|2024-12-01
|{{val|72.6|2.0}}
|SH0ES+CCHP JWST
|<ref>{{cite journal | doi=10.3847/1538-4357/ad8c21 | doi-access=free | title=JWST Validates HST Distance Measurements: Selection of Supernova Subsample Explains Differences in JWST Estimates of Local H <sub>0</sub> | date=2024 | last1=Riess | first1=Adam G. | last2=Scolnic | first2=Dan | last3=Anand | first3=Gagandeep S. | last4=Breuval | first4=Louise | last5=Casertano | first5=Stefano | last6=Macri | first6=Lucas M. | last7=Li | first7=Siyang | last8=Yuan | first8=Wenlong | last9=Huang | first9=Caroline D. | last10=Jha | first10=Saurabh | last11=Murakami | first11=Yukei S. | last12=Beaton | first12=Rachael | last13=Brout | first13=Dillon | last14=Wu | first14=Tianrui | last15=Addison | first15=Graeme E. | last16=Bennett | first16=Charles | last17=Anderson | first17=Richard I. | last18=Filippenko | first18=Alexei V. | last19=Carr | first19=Anthony | journal=The Astrophysical Journal | volume=977 | issue=1 | page=120 | arxiv=2408.11770 | bibcode=2024ApJ...977..120R }}</ref>
|JWST, 3 methods, Cepheids, TRGB, JAGB, 2 groups data
|-
|2023-07-19
|{{val|67.0|3.6}}
|Sneppen et al.
|<ref name="nature.com"/><ref name="aanda.org"/>
|Due to the blackbody spectra of the optical counterpart of neutron-star mergers, these systems provide strongly constraining estimators of cosmic distance. 
|-
|2023-07-13
|{{val|68.3|1.5}}
|[[South Pole Telescope#The SPT-3G camera|SPT-3G]]
|<ref>{{cite journal 
| last1=Balkenhol | first1=L. | last2=Dutcher | first2=D. | last3=Spurio Mancini | first3=A. | last4=Doussot | first4=A. | last5=Benabed | first5=K. | last6=Galli | first6=S. | collaboration=SPT-3G Collaboration 
| title=Measurement of the CMB temperature power spectrum and constraints on cosmology from the SPT-3G 2018 T T , T E , and E E dataset | journal=Physical Review D | volume=108 | issue=2 | date=2023-07-13 | page=023510 | issn=2470-0010 | doi=10.1103/PhysRevD.108.023510 | doi-access=free | arxiv=2212.05642 | bibcode=2023PhRvD.108b3510B }}</ref>
|CMB TT/TE/EE power spectrum. Less than 1''σ'' discrepancy with Planck.
|-
|2023-05-11
|{{val|66.6|4.1|3.3}}
|P. L. Kelly et al.
|<ref>{{Cite journal | first1=P. L. | last1=Kelly | first2=S. | last2=Rodney | first3=T. | last3=Treu | first4=M. | last4=Oguri | first5=W. | last5=Chen | first6=A. | last6=Zitri | display-authors=etal | date=2023-05-11 | journal=[[Science (journal)|Science]] | doi=10.1126/science.abh1322 | title=Constraints on the Hubble constant from Supernova Refsdal's reappearance| volume=380 | issue=6649 | article-number=eabh1322 | pmid=37167351 | arxiv=2305.06367 | bibcode=2023Sci...380.1322K | s2cid=258615332 }}</ref>
|Timing delay of gravitationally lensed images of [[SN Refsdal|Supernova Refsdal]]. Independent of cosmic distance ladder or the CMB.
|-
|2022-12-14
|{{val|67.3|10.0|9.1}}
|S. Contarini et al.
|<ref>{{Cite journal |last1=Contarini |first1=Sofia |last2=Pisani |first2=Alice |last3=Hamaus |first3=Nico |last4=Marulli |first4=Federico |last5=Moscardini |first5=Lauro |last6=Baldi |first6=Marco |date=2024 |title=The perspective of voids on rising cosmology tensions |journal=Astronomy & Astrophysics |volume=682 |article-number=A20 |doi=10.1051/0004-6361/202347572 |arxiv=2212.07438|bibcode=2024A&A...682A..20C }}</ref>
|Statistics of [[cosmic voids]] using [[Sloan Digital Sky Survey|BOSS]] DR12 data set.<ref>{{Cite web |last=Chiou |first=Lyndie |date=2023-07-25 |title=How (Nearly) Nothing Might Solve Cosmology's Biggest Questions |url=https://www.quantamagazine.org/how-nearly-nothing-might-solve-cosmologys-biggest-questions-20230725/ |access-date=2023-07-31 |website=Quanta Magazine |language=en}}</ref>
|-
|2022-02-08
|{{val|73.4|0.99|-1.22}}
|Pantheon+
|<ref>{{cite journal|last1=Brout|first1=Dillon|last2=Scolnic|first2=Dan|last3=Popovic|first3=Brodie|last4=Riess|first4=Adam G.|author4-link=Adam Riess|last5=Carr|first5=Anthony|last6=Zuntz|first6=Joe|last7=Kessler|first7=Rick|last8=Davis|first8=Tamara M.|last9=Hinton|first9=Samuel|last10=Jones|first10=David|last11=Kenworthy|first11=W. D'Arcy|last12=Peterson|first12=Erik R.|last13=Said|first13=Khaled|last14=Taylor|first14=Georgie|last15=Ali|first15=Noor|last16=Armstrong|first16=Patrick|last17=Charvu|first17=Pranav|last18=Dwomoh|first18=Arianna|last19=Meldorf|first19=Cole|last20=Palmese|first20=Antonella|last21=Qu|first21=Helen|last22=Rose|first22=Benjamin M.|last23=Sanchez|first23=Bruno|last24=Stubbs|first24=Christopher W.|last25=Vincenzi|first25=Maria|last26=Wood|first26=Charlotte M.|last27=Brown|first27=Peter J.|last28=Chen|first28=Rebecca|last29=Chambers|first29=Ken|last30=Coulter|first30=David A.|last31=Dai|first31=Mi|last32=Dimitriadis|first32=Georgios|last33=Filippenko|first33=Alexi V.|author33-link=Alex Filippenko|last34=Foley|first34=Ryan J.|last35=Jha|first35=Saurabh W.|last36=Kelsey|first36=Lisa|last37=Kirshner|first37=Robert P.|author37-link=Robert Kirshner|last38=Möller|first38=Anais|last39=Muir|first39=Jessie|last40=Nadathur|first40=Seshadri|last41=Pan|first41=Yen-Chen|last42=Rest|first42=Armin|last43=Rojas-Bravo|first43=Cesar|last44=Sako|first44=Masao|last45=Siebert|first45=Matthew R.|last46=Smith|first46=Mat|last47=Stahl|first47=Benjamin E.|last48=Wiseman|first48=Phil|date=2022-02-08|title=The Pantheon+ Analysis: Cosmological Constraints|journal=The Astrophysical Journal |volume=938 |issue=2 |page=110 |doi=10.3847/1538-4357/ac8e04 |arxiv=2202.04077|bibcode=2022ApJ...938..110B |s2cid=246679941 |doi-access=free }}</ref>
|[[Cosmic distance ladder#Type Ia light curves|SN Ia distance ladder]] (+SH0ES)
|-
|2022-06-17
|{{val|75.4|3.8|3.7}}
| T. de Jaeger et al.
|<ref name="deJaeger2022">{{cite journal |display-authors=4 |first1=T. |last1=de Jaeger |first2=L. |last2=Galbany |first3=A. G. |last3=Riess |first4=Ben E. |last4=Stahl |first5=B. J. |last5=Shappee |first6=A.V. |last6=Filippenko |first7=W. |last7=Zheng |title=A 5 per cent measurement of the Hubble–Lemaître constant from Type II supernovae |journal=MNRAS |date=17 June 2022 |volume=514 |issue=3 |pages=4620–4628 |doi=10.1093/mnras/stac1661 |doi-access=free |arxiv=2203.08974}}</ref>
| Use Type II supernovae as standardisable candles to obtain an independent measurement of the Hubble constant—13 SNe II with host-galaxy distances measured from Cepheid variables, the tip of the red giant branch, and geometric distance (NGC 4258).
|-
|2021-12-08
|{{val|73.04|1.04}}
|SH0ES
|<ref>{{cite journal|last1=Riess|first1=Adam G.|last2=Yuan|first2=Wenlong|last3=Macri|first3=Lucas M.|last4=Scolnic|first4=Dan|last5=Brout|first5=Dillon|last6=Casertano|first6=Stefano|last7=Jones|first7=David O.|last8=Murakami|first8=Yukei|last9=Breuval|first9=Louise|last10=Brink|first10=Thomas G.|last11=Filippenko|first11=Alexei V.|date=2021-12-08|title=A Comprehensive Measurement of the Local Value of the Hubble Constant with 1&nbsp;km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team|journal=The Astrophysical Journal |volume=934 |issue=1 |doi=10.3847/2041-8213/ac5c5b |arxiv=2112.04510|bibcode=2022ApJ...934L...7R |s2cid=245005861 |doi-access=free }}</ref>
|[[Cosmic distance ladder#Classical Cepheids|Cepheids]]-[[Cosmic distance ladder#Type Ia light curves|SN Ia distance ladder]] (HST+[[Gaia EDR3]]+"Pantheon+"). 5''σ'' discrepancy with planck.
|-
|2021-09-17
|{{val|69.8|1.7}}
|[[Wendy Freedman|W. Freedman]]
|<ref>{{Cite journal|last=Freedman|first=Wendy L.|date=2021-09-01|title=Measurements of the Hubble Constant: Tensions in Perspective*|journal=The Astrophysical Journal|volume=919|issue=1|article-number=16|doi=10.3847/1538-4357/ac0e95| arxiv=2106.15656|bibcode=2021ApJ...919...16F|s2cid=235683396|issn=0004-637X |doi-access=free }}</ref>
|[[Tip of the red-giant branch]] (TRGB) distance indicator (HST+Gaia EDR3)
|-
|2020-12-16
|{{val|72.1|2.0}}
| Hubble Space Telescope and [[Gaia EDR3]]
|<ref name="Soltis2020">{{cite journal | first1=J. |last1=Soltis |first2=S. |last2=Casertano |first3=A. G. |last3=Riess |title=The Parallax of Omega Centauri Measured from Gaia EDR3 and a Direct, Geometric Calibration of the Tip of the Red Giant Branch and the Hubble Constant |journal=The Astrophysical Journal |year=2021 |volume=908 |issue=1 |article-number=L5 |doi=10.3847/2041-8213/abdbad |arxiv=2012.09196|bibcode=2021ApJ...908L...5S |s2cid=229297709 |doi-access=free }}</ref>
| Combining earlier work on [[Red giant|red giant stars]], using the tip of the red-giant branch (TRGB) distance indicator, with [[parallax]] measurements of [[Omega Centauri]] from Gaia EDR3.
|-
|2020-12-15
|{{val|73.2|1.3}}
| Hubble Space Telescope and Gaia EDR3
|<ref name="Riess2020">{{cite journal |display-authors=4 |first1=A. G. |last1=Riess |first2=S. |last2=Casertano |first3=W. |last3=Yuan |first4=J. B. |last4=Bowers |first5=L. |last5=Macri |first6=J. C. |last6=Zinn |first7=D. |last7=Scolnic |title=Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with LambdaCDM |journal=The Astrophysical Journal |year=2021 |volume=908 |issue=1 |article-number=L6 |doi=10.3847/2041-8213/abdbaf |arxiv=2012.08534|bibcode=2021ApJ...908L...6R |s2cid=229213131 |doi-access=free }}</ref>
| Combination of HST [[Photometry (astronomy)|photometry]] and Gaia EDR3 parallaxes for Milky Way [[Cepheid variable|Cepheids]], reducing the uncertainty in calibration of Cepheid luminosities to 1.0%. Overall uncertainty in the value for {{math|''H''{{sub|0}}}} is 1.8%, which is expected to be reduced to 1.3% with a larger sample of type Ia supernovae in galaxies that are known Cepheid hosts. Continuation of a collaboration known as Supernovae, {{math|''H''{{sub|0}}}}, for the Equation of State of Dark Energy (SHoES).
|-
|2020-12-04
|{{val|73.5|5.3}}
| E. J. Baxter, B. D. Sherwin
|<ref name="Baxter2020">{{cite journal |first1=E. J. |last1=Baxter |first2=B. D. |last2=Sherwin |title=Determining the Hubble constant without the sound horizon scale: measurements from CMB lensing |date=February 2021 |journal=Monthly Notices of the Royal Astronomical Society |volume=501 |issue=2 |pages=1823–1835 |doi=10.1093/mnras/staa3706 |doi-access=free |arxiv=2007.04007|bibcode=2021MNRAS.501.1823B |s2cid=220404332 }}</ref>
| [[Gravitational lensing]] in the [[Cosmic Microwave Background|CMB]] is used to estimate {{math|''H''{{sub|0}}}} without referring to the [[Baryon acoustic oscillations#Cosmic sound|sound horizon scale]], providing an alternative method to analyze the Planck data.
|- 
|2020-11-25
|{{val|71.8|3.9|3.3}}
| P. Denzel et al.
|<ref name="Denzel2020">{{cite journal |first1=P. |last1=Denzel |first2=J. P. |last2=Coles |first3=P. |last3=Saha |first4=L. L. R. |last4=Williams |title=The Hubble constant from eight time-delay galaxy lenses |journal=Monthly Notices of the Royal Astronomical Society |volume=501 |issue=1 |date=February 2021 |pages=784–801 |doi=10.1093/mnras/staa3603 |doi-access=free |arxiv=2007.14398|bibcode=2021MNRAS.501..784D |s2cid=220845622 }}</ref>
| Eight quadruply [[Gravitational lensing|lensed]] galaxy systems are used to determine {{math|''H''{{sub|0}}}} to a precision of 5%, in agreement with both "early" and "late" universe estimates. Independent of distance ladders and the cosmic microwave background.
|-
|2020-11-07
|{{val|67.4|1.0}}
|T. Sedgwick et al.
|<ref>{{Cite journal|last1=Sedgwick|first1=Thomas M|last2=Collins|first2=Chris A|last3=Baldry|first3=Ivan K|last4=James|first4=Philip A|date=2020-11-07|title=The effects of peculiar velocities in SN Ia environments on the local H0 measurement|journal=Monthly Notices of the Royal Astronomical Society|volume=500|issue=3|pages=3728–3742|doi=10.1093/mnras/staa3456|doi-access=free | arxiv=1911.03155|issn=0035-8711}}</ref>
|Derived from 88 0.02 < {{mvar|z}} < 0.05 Type Ia supernovae used as standard candle distance indicators. The {{math|''H''{{sub|0}}}} estimate is corrected for the effects of peculiar velocities in the supernova environments, as estimated from the galaxy density field. The result assumes {{math|1= Ω{{sub|m}} = 0.3}}, {{math|1= Ω{{sub|Λ}} = 0.7}} and a sound horizon of {{val|149.3|u=Mpc}}, a value taken from Anderson et al. (2014).<ref>{{Cite journal|last1=Anderson|first1=Lauren|last2=Aubourg|first2=Éric|last3=Bailey|first3=Stephen|last4=Beutler|first4=Florian|last5=Bhardwaj|first5=Vaishali|last6=Blanton|first6=Michael|last7=Bolton|first7=Adam S.|last8=Brinkmann|first8=J.|last9=Brownstein|first9=Joel R.|last10=Burden|first10=Angela|last11=Chuang|first11=Chia-Hsun|date=2014-04-21|title=The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Releases 10 and 11 Galaxy samples|journal=Monthly Notices of the Royal Astronomical Society|volume=441|issue=1|pages=24–62|doi=10.1093/mnras/stu523|doi-access=free |issn=1365-2966|hdl=2445/101758|hdl-access=free}}</ref>
|-
|2020-09-29
|{{val|67.6|4.3|4.2}}
| S. Mukherjee et al.
|<ref name="Mukherjee2020">{{cite arXiv|display-authors=4 |first1=S. |last1=Mukherjee |first2=A. |last2=Ghosh |first3=M. J. |last3=Graham |first4=C. |last4=Karathanasis |first5=M. M. |last5=Kasliwal |first6=I. M. |last6=Hernandez |first7=S. M. |last7=Nissanke |first8=A. |last8=Silvestri |first9=B. D. |last9=Wandelt |title=First measurement of the Hubble parameter from bright binary black hole GW190521 |date=29 September 2020 |class=astro-ph.CO |eprint=2009.14199}}</ref>
| [[Gravitational wave]]s, assuming that the transient ZTF19abanrh found by the [[Zwicky Transient Facility]] is the optical counterpart to [[GW190521]]. Independent of distance ladders and the cosmic microwave background.
|-
|2020-06-18
|{{val|75.8|5.2|4.9}}
| T. de Jaeger et al.
|<ref name="deJaeger2020">{{cite journal |display-authors=4 |first1=T. |last1=de Jaeger |first2=B. |last2=Stahl |first3=W. |last3=Zheng |first4=A.V. |last4=Filippenko |first5=A. G. |last5=Riess |first6=L. |last6=Galbany |title=A measurement of the Hubble constant from Type II supernovae |journal=MNRAS |date=18 June 2020 |volume=496 |issue=3 |pages=3402–3411 |doi=10.1093/mnras/staa1801 |doi-access=free |arxiv=2006.03412}}</ref>
| Use Type II supernovae as standardisable candles to obtain an independent measurement of the Hubble constant—7 SNe II with host-galaxy distances measured from Cepheid variables or the tip of the red giant branch.
|-
|2020-02-26
|{{val|73.9|3.0}}
| Megamaser Cosmology Project
|<ref name="megamaser">{{cite journal |display-authors=4 |last1=Pesce |first1=D. W. |last2=Braatz |first2=J. A. |last3=Reid |first3=M. J. |last4=Riess |first4=A. G. |last5=Scolnic |first5=D. |last6=Condon |first6=J. J. |last7=Gao |first7=F. |last8=Henkel |first8=C. |last9=Impellizzeri |first9=C. M. V. |last10=Kuo |first10=C. Y. |last11=Lo |first11=K. Y. |title=The Megamaser Cosmology Project. XIII. Combined Hubble Constant Constraints |journal=The Astrophysical Journal |date=26 February 2020 |volume=891 |issue=1 |article-number=L1 |doi=10.3847/2041-8213/ab75f0 |arxiv=2001.09213 |bibcode=2020ApJ...891L...1P |s2cid=210920444 |doi-access=free }}</ref>
| Geometric distance measurements to megamaser-hosting galaxies. Independent of distance ladders and the cosmic microwave background.
|-
|2019-10-14
|{{val|74.2|2.7|3.0}}
| STRIDES
|<ref>{{cite journal |display-authors=4 |last1=Shajib |first1=A. J. |last2=Birrer |first2=S. |last3=Treu |first3=T. |last4=Agnello |first4=A. |last5=Buckley-Geer |first5=E. J. |last6=Chan |first6=J. H. H. |last7=Christensen |first7=L. |last8=Lemon |first8=C. |last9=Lin |first9=H. |last10=Millon |first10=M. |last11=Poh |first11=J. |last12=Rusu |first12=C. E. |last13=Sluse |first13=D. |last14=Spiniello |first14=C. |last15=Chen |first15=G. C.-F. |last16=Collett |first16=T. |last17=Courbin |first17=F. |last18=Fassnacht |first18=C. D. |last19=Frieman |first19=J. |last20=Galan |first20=A. |last21=Gilman |first21=D. |last22=More |first22=A. |last23=Anguita |first23=T. |last24=Auger |first24=M. W. |last25=Bonvin |first25=V. |last26=Meylan |first26=G. |last27=Wong |first27=K. C. |last28=Abbott |first28=T. M. C. |last29=Annis |first29=J. |last30=Avila |first30=S. |last31=Bechtol |first31=K. |last32=Brooks |first32=D. |last33=Brout |first33=D. |last34=Burke |first34=D. L. |last35=Rosell |first35=A. Carnero |last36=Kind |first36=M. Carrasco |last37=Carretero |first37=J. |last38=Castander |first38=F. J. |last39=Costanzi |first39=M. |last40=da Costa |first40=L. N. |last41=De Vicente |first41=J. |last42=Desai |first42=S. |last43=Dietrich |first43=J. P. |last44=Doel |first44=P. |last45=Drlica-Wagner |first45=A. |last46=Evrard |first46=A. E. |last47=Finley |first47=D. A. |last48=Flaugher |first48=B. |last49=Fosalba |first49=P. |last50=García-Bellido |first50=J. |last51=Gerdes |first51=D. W. |last52=Gruen |first52=D. |last53=Gruendl |first53=R. A. |last54=Gschwend |first54=J. |last55=Gutierrez |first55=G. |last56=Hollowood |first56=D. L. |last57=Honscheid |first57=K. |last58=Huterer |first58=D. |last59=James |first59=D. J. |last60=Jeltema |first60=T. |last61=Krause |first61=E. |last62=Kuropatkin |first62=N. |last63=Li |first63=T. S. |last64=Lima |first64=M. |last65=MacCrann |first65=N. |last66=Maia |first66=M. A. G. |last67=Marshall |first67=J. L. |last68=Melchior |first68=P. |last69=Miquel |first69=R. |last70=Ogando |first70=R. L. C. |last71=Palmese |first71=A. |last72=Paz-Chinchón |first72=F. |last73=Plazas |first73=A. A. |last74=Romer |first74=A. K. |last75=Roodman |first75=A. |last76=Sako |first76=M. |last77=Sanchez |first77=E. |last78=Santiago |first78=B. |last79=Scarpine |first79=V. |last80=Schubnell |first80=M. |last81=Scolnic |first81=D. |last82=Serrano |first82=S. |last83=Sevilla-Noarbe |first83=I. |last84=Smith |first84=M. |last85=Soares-Santos |first85=M. |last86=Suchyta |first86=E. |last87=Tarle |first87=G. |last88=Thomas |first88=D. |last89=Walker |first89=A. R. |last90=Zhang |first90=Y. |title=STRIDES: A 3.9 per cent measurement of the Hubble constant from the strongly lensed system DES J0408-5354 |date=14 October 2019 |journal=Monthly Notices of the Royal Astronomical Society |volume=494 |issue=4 |doi=10.1093/mnras/staa828 |doi-access=free |arxiv=1910.06306 |s2cid=204509190 }}</ref>
| Modelling the mass distribution & time delay of the lensed [[quasar]] DES J0408-5354.
|-
|2019-09-12
|{{val|76.8|2.6}}
| SHARP/H0LiCOW
|<ref>{{cite journal |display-authors=4 |last1=Chen |first1=G.C.-F. |last2=Fassnacht |first2=C.D. |last3=Suyu |first3=S.H.|author3-link=Sherry Suyu |last4=Rusu |first4=C.E. |last5=Chan |first5=J.H.H. |last6=Wong |first6=K.C. |last7=Auger |first7=M.W. |last8=Hilbert |first8=S. |last9=Bonvin |first9=V. |last10=Birrer |first10=S. |last11=Millon |first11=M. |last12=Koopmans |first12=L.V.E. |last13=Lagattuta |first13=D.J. |last14=McKean |first14=J.P. |last15=Vegetti |first15=S. |last16=Courbin |first16=F. |last17=Ding |first17=X. |last18=Halkola |first18=A. |last19=Jee |first19=I. |last20=Shajib |first20=A.J. |last21=Sluse |first21=D. |last22=Sonnenfeld |first22=A. |last23=Treu |first23=T. |title=A SHARP view of H0LiCOW: H0 from three time-delay gravitational lens systems with adaptive optics imaging |journal=Monthly Notices of the Royal Astronomical Society |volume=490 |issue=2 |pages=1743–1773 |date=12 September 2019 |language=en|arxiv=1907.02533|doi=10.1093/mnras/stz2547 |doi-access=free |bibcode=2019MNRAS.490.1743C |s2cid=195820422 }}</ref>
| Modelling three galactically lensed objects and their lenses using ground-based adaptive optics and the Hubble Space Telescope.
|-
|2019-08-20
|{{val|73.3|+1.36|-1.35}}
|K. Dutta et al.
|<ref>{{cite journal |first1=Koushik |last1=Dutta |first2=Anirban |last2=Roy |first3=Ruchika|last3=Ruchika|first4= Anjan A. |last4=Sen |first5=M. M.|last5= Sheikh-Jabbari|title=Cosmology With Low-Redshift Observations: No Signal For New Physics|journal=Phys. Rev. D|volume=100 |issue=10 |article-number=103501 |date=20 August 2019 |language=en |arxiv=1908.07267 |doi=10.1103/PhysRevD.100.103501 |bibcode=2019PhRvD.100j3501D|s2cid=201107151 }}</ref>
|This <math>H_0</math> is obtained analysing low-redshift cosmological data within ΛCDM model. The datasets used are type-Ia supernovae, [[baryon acoustic oscillations]], time-delay measurements using strong-lensing, {{math|''H''(''z'')}} measurements using cosmic chronometers and growth measurements from large scale structure observations.
|-
|2019-08-15
|{{val|73.5|1.4}}
| M. J. Reid, D. W. Pesce, A. G. Riess
|<ref>{{cite journal |first1=M. J. |last1=Reid |first2=D. W. |last2=Pesce |first3=A. G. |last3=Riess |title=An Improved Distance to NGC 4258 and its Implications for the Hubble Constant |journal=The Astrophysical Journal |volume=886 |issue=2 |article-number=L27 |date=15 August 2019 |language=en |arxiv=1908.05625 |doi=10.3847/2041-8213/ab552d |bibcode=2019ApJ...886L..27R |s2cid=199668809 |doi-access=free }}</ref>
| Measuring the distance to [[Messier 106]] using its supermassive black hole, combined with measurements of eclipsing binaries in the Large Magellanic Cloud.
|-
|2019-07-16
|{{val|69.8|1.9}}
|Hubble Space Telescope
|<ref name="EA-20190716">{{cite news |author=Carnegie Institution of Science |author-link=Carnegie Institution of Science |date=16 July 2019 |title=New measurement of universe's expansion rate is 'stuck in the middle' – Red giant stars observed by Hubble Space Telescope used to make an entirely new measurement of how fast the universe is expanding |work=[[EurekAlert!]] |url=https://www.eurekalert.org/pub_releases/2019-07/cifs-nmo071619.php |access-date=16 July 2019}}</ref><ref name="SCI-20190719">{{cite journal |last=Sokol |first=Joshua |title=Debate intensifies over speed of expanding universe |url=https://www.science.org/content/article/debate-intensifies-over-speed-expanding-universe |date=19 July 2019 |journal=[[Science (journal)|Science]] |doi=10.1126/science.aay8123 |s2cid=200021863 |access-date=20 July 2019 }}</ref><ref name="The Carnegie-Chicago Hubble Program"/>
|Distances to red giant stars are calculated using the tip of the red-giant branch (TRGB) distance indicator.
|-
|2019-07-10
|{{val|73.3|+1.7|-1.8}}
|[[H0LiCOW]] collaboration
|<ref name="H0LiCOW2019">{{cite journal|arxiv=1907.04869|author1=Kenneth C. Wong|title=H0LiCOW XIII. A 2.4% measurement of ''H''<sub>0</sub> from lensed quasars: 5.3''σ'' tension between early and late-Universe probes|journal=Monthly Notices of the Royal Astronomical Society|year=2020|volume=498 |issue=1 |doi=10.1093/mnras/stz3094|doi-access=free |s2cid=195886279}}</ref>
|Updated observations of multiply imaged quasars, now using six quasars, independent of the cosmic distance ladder and independent of the cosmic microwave background measurements.
|-
|2019-07-08
|{{val|70.3|5.3|5.0}}
|The [[LIGO Scientific Collaboration]] and The [[Virgo interferometer|Virgo]] Collaboration
|<ref name="NAT-20190708" />
|Uses radio counterpart of GW170817, combined with earlier gravitational wave (GW) and [[electromagnetic]] (EM) data.
|-
|2019-03-28
|{{val|68.0|4.2|4.1}}
|[[Fermi Gamma-ray Space Telescope|Fermi-LAT]]
|<ref>{{cite journal|arxiv=1903.12097|first1=Alberto|last1=Domínguez|first2=Radoslaw|last2=Wojtak|display-authors=1|title=A new measurement of the Hubble constant and matter content of the Universe using extragalactic background light γ-ray attenuation|journal=The Astrophysical Journal|volume=885|issue=2|article-number=137|date=28 March 2019|bibcode=2019ApJ...885..137D|doi=10.3847/1538-4357/ab4a0e|s2cid=85543845 |doi-access=free }}</ref>
|Gamma ray attenuation due to extragalactic light. Independent of the cosmic distance ladder and the cosmic microwave background.
|-
|-
|2019-03-18
|{{val|74.03|1.42}}
|Hubble Space Telescope
|<ref name="Riess2019">{{cite journal|arxiv=1903.07603|first1=Adam G.|last1=Riess|first2=Stefano|last2=Casertano|first3=Wenlong|last3=Yuan|first4=Lucas M.|last4=Macri|first5=Dan|last5=Scolnic|title=Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM |journal=The Astrophysical Journal|volume=876|issue=1|article-number=85|date=18 March 2019|doi=10.3847/1538-4357/ab1422|bibcode=2019ApJ...876...85R|s2cid=85528549 |doi-access=free }}</ref>
|Precision HST photometry of Cepheids in the [[Large Magellanic Cloud|Large Magellanic Cloud (LMC)]] reduce the uncertainty in the distance to the LMC from 2.5% to 1.3%. The revision increases the tension with [[Cosmic microwave background|CMB]] measurements to the 4.4''σ'' level (P=99.999% for Gaussian errors), raising the discrepancy beyond a plausible level of chance. Continuation of a collaboration known as Supernovae, {{math|''H''{{sub|0}}}}, for the Equation of State of Dark Energy (SHoES).
|-
|2019-02-08
|{{val|67.78|0.91|0.87}}
|[[Joseph Ryan (astrophysicist)|Joseph Ryan]] et al.
|<ref name="Ryan2019">{{Cite journal|title=Baryon acoustic oscillation, Hubble parameter, and angular size measurement constraints on the Hubble constant, dark energy dynamics, and spatial curvature|journal=Monthly Notices of the Royal Astronomical Society|volume=488|issue=3|pages=3844–3856|first1=Joseph|last1=Ryan|first2=Yun|last2=Chen|first3=Bharat|last3=Ratra |arxiv=1902.03196|date=8 February 2019|doi=10.1093/mnras/stz1966|doi-access=free |bibcode=2019MNRAS.488.3844R|s2cid=119226802}}</ref>
|Quasar angular size and baryon acoustic oscillations, assuming a flat ΛCDM model. Alternative models result in different (generally lower) values for the Hubble constant.
|-
|2018-11-06
|{{val|67.77|1.30}}
|[[Dark Energy Survey]]
|<ref name="DES">{{cite journal|arxiv=1811.02376|last1=Macaulay|first1=E|last2=Nichol|first2=R.C|display-authors=1|title=First Cosmological Results using Type Ia Supernovae from the Dark Energy Survey: Measurement of the Hubble Constant|journal=Monthly Notices of the Royal Astronomical Society|volume=486|issue=2|pages=2184–2196|collaboration=DES collaboration|year=2018|doi=10.1093/mnras/stz978|doi-access=free |s2cid=119310644}}</ref>
|Supernova measurements using the ''inverse distance ladder'' method based on baryon acoustic oscillations.
|-
|2018-09-05
|{{val|72.5|+2.1|-2.3}}
|H0LiCOW collaboration
|<ref name="H0LiCOW">{{cite journal |last1=Birrer |first1=S. |last2=Treu |first2=T. |last3=Rusu |first3=C. E. |last4=Bonvin |first4=V. |last5=Fassnacht |first5=C. D. |last6=Chan |first6=J. H. H. |last7=Agnello |first7=A. |last8=Shajib |first8=A. J. |last9=Chen |first9=G. C. -F. |last10=Auger |first10=M. |last11=Courbin |first11=F. |last12=Hilbert |first12=S. |last13=Sluse |first13=D. |last14=Suyu |first14=S. H.|author14-link=Sherry Suyu |last15=Wong |first15=K. C. |display-authors=6 |year=2018 |title=H0LiCOW – IX. Cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 and a new measurement of the Hubble constant |journal=Monthly Notices of the Royal Astronomical Society |volume=484 |issue=4 |pages=4726–4753 |arxiv=1809.01274 |bibcode=2019MNRAS.484.4726B |doi=10.1093/mnras/stz200 |s2cid=119053798 |last16=Marshall |first16=P |last17=Lemaux |first17=B. C |last18=Meylan |first18=G|doi-access=free }}</ref>
|Observations of multiply imaged quasars, independent of the cosmic distance ladder and independent of the cosmic microwave background measurements.
|-
|2018-07-18
|{{val|67.66|0.42}}
|[[Planck (spacecraft)#2018 final data release|Planck Mission]]
|<ref name="2018planckcosmos">{{cite journal |title=Planck 2018 results. VI. Cosmological parameters |bibcode=2020A&A...641A...6P |author1=Planck Collaboration |last2=Aghanim |first2=N. |journal=Astronomy and Astrophysics |author2-link=Nabila Aghanim|display-authors=etal |year=2018 |volume=641 |article-number=A6 |doi=10.1051/0004-6361/201833910 |arxiv=1807.06209 }}</ref>
|Final Planck 2018 results.
|-
|2018-04-27
|{{val|73.52|1.62}}
|Hubble Space Telescope and [[Gaia (spacecraft)|Gaia]]
|<ref name="gaiariess2018">{{cite journal |display-authors=4 |last1=Riess |first1=Adam G. |last2=Casertano |first2=Stefano |last3=Yuan |first3=Wenlong |last4=Macri |first4=Lucas |last5=Bucciarelli |first5=Beatrice |last6=Lattanzi |first6=Mario G. |last7=MacKenty |first7=John W. |last8=Bowers |first8=J. Bradley |last9=Zheng |first9=WeiKang |last10=Filippenko |first10=Alexei V. |last11=Huang |first11=Caroline |last12=Anderson |first12=Richard I. |title=Milky Way Cepheid Standards for Measuring Cosmic Distances and Application to Gaia DR2: Implications for the Hubble Constant |arxiv=1804.10655|journal=The Astrophysical Journal |date=2018 |volume=861 |issue=2 |article-number=126 |doi=10.3847/1538-4357/aac82e |language=en |issn=0004-637X|bibcode=2018ApJ...861..126R |s2cid=55643027 |doi-access=free }}</ref><ref name="guardianhubbleconstant">{{cite news|last1=Devlin|first1=Hannah|title=The answer to life, the universe and everything might be 73. Or 67|url=https://www.theguardian.com/science/2018/may/10/the-answer-to-life-the-universe-and-everything-might-be-73-or-67|access-date=13 May 2018|work=the Guardian|date=10 May 2018|language=en}}</ref>
|Additional HST [[Photometry (astronomy)|photometry]] of galactic Cepheids with early Gaia parallax measurements. The revised value increases tension with CMB measurements at the 3.8''σ'' level. Continuation of the SHoES collaboration.
|-
|2018-02-22
|{{val|73.45|1.66}}
|Hubble Space Telescope
|<ref>{{Cite journal |display-authors=4 |last1=Riess |first1=Adam G. |last2=Casertano |first2=Stefano |last3=Yuan |first3=Wenlong |last4=Macri |first4=Lucas |last5=Anderson |first5=Jay |last6=MacKenty |first6=John W.|last7=Bowers |first7=J. Bradley |last8=Clubb |first8=Kelsey I. |last9=Filippenko |first9=Alexei V. |last10=Jones |first10=David O. |last11=Tucker |first11=Brad E. |title=New parallaxes of galactic Cepheids from spatially scanning the Hubble Space Telescope: Implications for the Hubble constant |journal=The Astrophysical Journal |volume=855 |issue=2 |article-number=136 |date=22 February 2018 |bibcode=2018ApJ...855..136R |arxiv=1801.01120 |doi=10.3847/1538-4357/aaadb7 |s2cid=67808349 |doi-access=free }}</ref><ref name="NASA-20180222">{{cite web |last1=Weaver |first1=Donna |last2=Villard |first2=Ray |last3=Hille |first3=Karl |title=Improved Hubble Yardstick Gives Fresh Evidence for New Physics in the Universe |url=https://www.nasa.gov/feature/goddard/2018/improved-hubble-yardstick-gives-fresh-evidence-for-new-physics-in-the-universe |date=22 February 2018 |website=[[NASA]] |access-date=24 February 2018 }}</ref>
|Parallax measurements of galactic Cepheids for enhanced calibration of the [[Cosmic distance ladder|distance ladder]]; the value suggests a discrepancy with CMB measurements at the 3.7''σ'' level. The uncertainty is expected to be reduced to below 1% with the final release of the Gaia catalog. SHoES collaboration.
|-
|2017-10-16
|{{val|70.0|+12.0|-8.0}}
|The [[LIGO Scientific Collaboration]] and The [[Virgo interferometer|Virgo]] Collaboration
|<ref>{{Cite journal
| last1=Foley | first1=R. J.  | last2=Annis | first2=J.  | last3=Tanvir | first3=N. R. T 
|collaboration=The LIGO Scientific Collaboration and The Virgo Collaboration, The 1M2H Collaboration, The Dark Energy Camera GW-EM Collaboration and the DES Collaboration, The DLT40 Collaboration, The Las Cumbres Observatory Collaboration, The VINROUGE Collaboration & The MASTER Collaboration
| title=A gravitational-wave standard siren measurement of the Hubble constant | journal=Nature | volume=551 | issue=7678 | date=2017-10-16 | issn=0028-0836 | doi=10.1038/nature24471 | doi-access=free | pages=85–88 | pmid=29094696 | arxiv=1710.05835 | bibcode=2017Natur.551...85A }}</ref>
| [[Cosmic distance ladder#Standard siren|Standard siren]] measurement independent of normal "standard candle" techniques; the gravitational wave analysis of a binary [[neutron star]] (BNS) merger [[GW170817]] directly estimated the luminosity distance out to cosmological scales. An estimate of fifty similar detections in the next decade may arbitrate tension of other methodologies.<ref>{{cite journal |display-authors=4 |arxiv=1802.03404 |title=Prospects for resolving the Hubble constant tension with standard sirens |journal=Physical Review Letters |volume=122 |issue=6 |article-number=061105 |last1=Feeney |first1=Stephen M |last2=Peiris |first2=Hiranya V |last3=Williamson |first3=Andrew R |last4=Nissanke |first4=Samaya M |last5=Mortlock |first5=Daniel J |last6=Alsing |first6=Justin |last7=Scolnic |first7=Dan |year=2019 |bibcode=2019PhRvL.122f1105F |doi=10.1103/PhysRevLett.122.061105 |pmid=30822066 |url=https://repository.ubn.ru.nl/handle/2066/201510|hdl=2066/201510 |s2cid=73493934 }}</ref> Detection and analysis of a neutron star-black hole merger (NSBH) may provide greater precision than BNS could allow.<ref name="VitaleChen2018">{{cite journal |last1=Vitale |first1=Salvatore |last2=Chen |first2=Hsin-Yu |title=Measuring the Hubble Constant with Neutron Star Black Hole Mergers |journal=Physical Review Letters |date=12 July 2018 |volume=121 |issue=2 |article-number=021303 |doi=10.1103/PhysRevLett.121.021303 |pmid=30085719 |arxiv=1804.07337 |bibcode=2018PhRvL.121b1303V |hdl=1721.1/117110 |s2cid=51940146 }}</ref>
|-
|2016-11-22
|{{val|71.9|+2.4|-3.0}}
|Hubble Space Telescope
|<ref>{{Cite journal |first1=Vivien |last1=Bonvin |first2=Frédéric |last2=Courbin |first3=Sherry H. |last3=Suyu |author3-link=Sherry Suyu|display-authors=etal |date=2016-11-22 |title=H0LiCOW – V. New COSMOGRAIL time delays of HE 0435−1223: ''H''<sub>0</sub> to 3.8 per cent precision from strong lensing in a flat ΛCDM model |journal=[[MNRAS]] |volume=465 |issue=4 |pages=4914–4930 |doi=10.1093/mnras/stw3006 |doi-access=free |arxiv=1607.01790
|bibcode = 2017MNRAS.465.4914B |s2cid=109934944 }}</ref>
| Uses time delays between multiple images of distant variable sources produced by [[strong gravitational lensing]]. Collaboration known as {{math|''H''{{sub|0}}}} Lenses in COSMOGRAIL's Wellspring (H0LiCOW).
|-
|2016-08-04
|{{val|76.2|+3.4|-2.7}}
| Cosmicflows-3
| <ref name="Cosmicflows-3">{{cite journal |last1=Tully |first1=R. Brent |last2=Courtois |first2=Hélène M. |last3=Sorce |first3=Jenny G. |title=COSMICFLOWS-3 |journal=The Astronomical Journal |date=3 August 2016 |volume=152 |issue=2 |article-number=50 |doi=10.3847/0004-6256/152/2/50 |arxiv=1605.01765 |bibcode=2016AJ....152...50T |s2cid=250737862 |doi-access=free }}</ref>
| Comparing redshift to other distance methods, including [[Tully–Fisher relation|Tully–Fisher]], Cepheid variable, and Type Ia supernovae. A restrictive estimate from the data implies a more precise value of {{val|75|2}}.
|-
|2016-07-13
|{{val|67.6|+0.7|-0.6}}
|[[Sloan Digital Sky Survey|SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS)]]
|<ref>{{Cite journal|last1=Grieb|first1=Jan N.|last2=Sánchez|first2=Ariel G.|last3=Salazar-Albornoz|first3=Salvador|date=2016-07-13|title=The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological implications of the Fourier space wedges of the final sample |arxiv=1607.03143|doi=10.1093/mnras/stw3384|journal=Monthly Notices of the Royal Astronomical Society|volume=467|issue=2|pages=2085–2112 |doi-access=free |bibcode = 2017MNRAS.467.2085G |s2cid=55888085}}</ref>
|Baryon acoustic oscillations. An extended survey (eBOSS) began in 2014 and is expected to run through 2020. The extended survey is designed to explore the time when the universe was transitioning away from the deceleration effects of gravity from 3 to 8 billion years after the Big Bang.<ref name="ebossinfo">{{cite web|title=The Extended Baryon Oscillation Spectroscopic Survey (eBOSS)|url=http://www.sdss.org/surveys/eboss/|website=SDSS|access-date=13 May 2018}}</ref>
|-
|2016-05-17
|{{val|73.24|1.74}}
|Hubble Space Telescope
|<ref>{{Cite journal|display-authors=4|last1=Riess|first1=Adam G.|last2=Macri|first2=Lucas M.|last3=Hoffmann|first3=Samantha L.|last4=Scolnic|first4=Dan|last5=Casertano|first5=Stefano|last6=Filippenko|first6=Alexei V.|last7=Tucker|first7=Brad E.|last8=Reid|first8=Mark J.|last9=Jones|first9=David O.|date=2016-04-05|title=A 2.4% Determination of the Local Value of the Hubble Constant|arxiv=1604.01424|doi=10.3847/0004-637X/826/1/56|volume=826|issue=1|journal=The Astrophysical Journal|page=56|bibcode = 2016ApJ...826...56R |s2cid=118630031 |doi-access=free }}</ref>
|[[Type Ia supernova]], the uncertainty is expected to go down by a factor of more than two with upcoming Gaia measurements and other improvements. SHoES collaboration.
|-
| 2015-02
| {{val|67.74|0.46}}
| [[Planck (spacecraft)#2015 data release|Planck Mission]]
| <ref name="planckesa2015">{{cite web |url=http://www.cosmos.esa.int/web/planck/publications |title=Planck Publications: Planck 2015 Results |publisher=European Space Agency |date=February 2015 |access-date=9 February 2015}}</ref><ref name="nature20141202">{{cite news |url=http://www.nature.com/news/european-probe-shoots-down-dark-matter-claims-1.16462 |title=European probe shoots down dark-matter claims |journal=Nature |first1=Ron |last1=Cowen |first2=Davide |last2=Castelvecchi |date=2 December 2014 |access-date=6 December 2014 |doi=10.1038/nature.2014.16462}}</ref>
| Results from an analysis of ''Planck''{{'}}s full mission were made public on 1 December 2014 at a conference in [[Ferrara]], Italy. A full set of papers detailing the mission results were released in February 2015.
|-
| 2013-10-01
| {{val|74.4|3.0}}
| Cosmicflows-2
| <ref name="cosmicflows2">{{cite journal|display-authors=4|last1=Tully|first1=R. Brent|last2=Courtois|first2=Helene M.|last3=Dolphin|first3=Andrew E.|last4=Fisher|first4=J. Richard|last5=Héraudeau|first5=Philippe|last6=Jacobs|first6=Bradley A.|last7=Karachentsev|first7=Igor D.|last8=Makarov|first8=Dmitry|last9=Makarova|first9=Lidia|last10=Mitronova|first10=Sofia|last11=Rizzi|first11=Luca|last12=Shaya|first12=Edward J.|last13=Sorce|first13=Jenny G.|last14=Wu|first14=Po-Feng|title=Cosmicflows-2: The Data|journal=The Astronomical Journal|date=5 September 2013|volume=146|issue=4|article-number=86|doi=10.1088/0004-6256/146/4/86|issn=0004-6256|arxiv=1307.7213|bibcode=2013AJ....146...86T|s2cid=118494842}}</ref>
| Comparing redshift to other distance methods, including Tully–Fisher, Cepheid variable, and Type Ia supernovae.
|-
| 2013-03-21
| {{val|67.80|0.77}}
| [[Planck (spacecraft)#2013 data release|Planck Mission]]
| <ref name="planck_overview">{{cite journal |last=Bucher |first=P. A. R. |author2=''et al.'' ([[Planck Collaboration]]) |date=2013 |title=Planck 2013 results. I. Overview of products and scientific Results |arxiv=1303.5062 |doi=10.1051/0004-6361/201321529 |volume=571 |journal=Astronomy & Astrophysics |page=A1 |bibcode=2014A&A...571A...1P |s2cid=218716838 }}</ref><ref name="ESA-20130321">{{cite web |date=21 March 2013 |title=Planck reveals an almost perfect universe |url=http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe |publisher=[[European Space Agency|ESA]] |access-date=2013-03-21 }}</ref><ref name="NASA-20130321">{{cite web |title=Planck Mission Brings Universe Into Sharp Focus |url=http://www.jpl.nasa.gov/news/news.php?release=2013-109&rn=news.xml&rst=3739 |date=21 March 2013 |publisher=[[Jet Propulsion Laboratory|JPL]] |access-date=2013-03-21 }}</ref><ref name="NYT-20130321">{{cite news |last=Overbye |first=D. |title=An infant universe, born before we knew |url=https://www.nytimes.com/2013/03/22/science/space/planck-satellite-shows-image-of-infant-universe.html |date=21 March 2013 |work=[[New York Times]] |access-date=2013-03-21 }}</ref><ref name="NBC-20130321">{{cite web |last=Boyle |first=A. |date=21 March 2013 |title=Planck probe's cosmic 'baby picture' revises universe's vital statistics |url=http://cosmiclog.nbcnews.com/_news/2013/03/21/17397298-planck-probes-cosmic-baby-picture-revises-universes-vital-statistics |website=[[NBC News]] |access-date=2013-03-21 |archive-date=2013-03-23 |archive-url=https://web.archive.org/web/20130323235242/http://cosmiclog.nbcnews.com/_news/2013/03/21/17397298-planck-probes-cosmic-baby-picture-revises-universes-vital-statistics |url-status=dead }}</ref>
| The [[European Space Agency|ESA]] Planck Surveyor was launched in May 2009. Over a four-year period, it performed a significantly more detailed investigation of cosmic microwave radiation than earlier investigations using [[High-electron-mobility transistor|HEMT]] [[radiometer]]s and [[bolometer]] technology to measure the CMB at a smaller scale than WMAP. On 21 March 2013, the European-led research team behind the Planck cosmology probe released the mission's data including a new CMB all-sky map and their determination of the Hubble constant.
|-
| 2012-12-20
| {{val|69.32|0.80}}
| [[Wilkinson Microwave Anisotropy Probe|WMAP]] (9 years), combined with other measurements
| <ref>{{cite journal |last1=Bennett |first1=C. L. |display-authors=etal |date=2013 |title=Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Final maps and results |journal=[[The Astrophysical Journal Supplement Series]] |volume=208 |issue=2 |article-number=20 |arxiv=1212.5225 |bibcode=2013ApJS..208...20B |doi=10.1088/0067-0049/208/2/20 |s2cid=119271232 }}</ref>
|
|-
| 2010
| {{val|70.4|+1.3|-1.4}}
| WMAP (7 years), combined with other measurements
| <ref name="wmap7parameters">{{cite journal |last1=Jarosik |first1=N. |display-authors=etal |date=2011 |title=Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Sky maps, systematic errors, and basic results |journal=[[The Astrophysical Journal Supplement Series]] |volume=192 |issue=2 |article-number=14 |arxiv=1001.4744 |bibcode=2011ApJS..192...14J |doi=10.1088/0067-0049/192/2/14 |s2cid=46171526 }}</ref>
| These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the ΛCDM model. If the data are fit with more general versions, {{math|''H''{{sub|0}}}} tends to be smaller and more uncertain: typically around {{val|67|4|u=km/s|up=Mpc}} although some models allow values near {{val|63|u=km/s|up=Mpc}}.<ref>Results for {{math|''H''{{sub|0}}}} and other cosmological parameters obtained by fitting a variety of models to several combinations of WMAP and other data are available at the [[NASA]]'s [http://lambda.gsfc.nasa.gov/product/map/current/parameters.cfm LAMBDA website] {{Webarchive|url=https://web.archive.org/web/20140709010232/http://lambda.gsfc.nasa.gov/product/map/current/parameters.cfm |date=2014-07-09 }}.</ref>
|-
| 2010
| {{val|71.0|2.5}}
| WMAP only (7 years).
| <ref name="wmap7parameters"/>
|
|-
| 2009-02
| {{val|70.5|1.3}}
| WMAP (5 years), combined with other measurements
| <ref name="WMAP2009">{{cite journal |last=Hinshaw |first=G. |author2=et al. (WMAP Collaboration) |year=2009 |title=Five-year Wilkinson Microwave Anisotropy Probe observations: Data processing, sky maps, and basic results |journal=[[The Astrophysical Journal Supplement]] |volume=180 |issue=2 |pages=225–245 |arxiv=0803.0732 |bibcode=2009ApJS..180..225H |doi=10.1088/0067-0049/180/2/225 |s2cid=3629998 }}</ref>
|
|-
| 2009-02
| {{val|71.9|2.6|-2.7}}
| WMAP only (5 years)
| <ref name="WMAP2009"/>
|
|-
| 2007
| {{val|70.4|1.5|-1.6}}
| WMAP (3 years), combined with other measurements
| <ref>{{Cite journal |last=Spergel |first=D. N. |author2=et al. (WMAP Collaboration) |year=2007 |title=Three-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for cosmology |journal=[[The Astrophysical Journal Supplement Series]] |volume=170 |issue=2 |pages=377–408 |arxiv=astro-ph/0603449 |bibcode=2007ApJS..170..377S |doi=10.1086/513700 |s2cid=1386346 }}</ref>
|
|-
| 2006-08
| {{val|76.9|+10.7|-8.7}}
| [[Chandra X-ray Observatory]]
| <ref>{{cite journal |display-authors=4 |last1=Bonamente |first1=M. |last2=Joy |first2=M. K. |last3=Laroque |first3=S. J. |last4=Carlstrom |first4=J. E. |last5=Reese |first5=E. D. |last6=Dawson |first6=K. S. |date=2006 |title=Determination of the cosmic distance scale from Sunyaev–Zel'dovich effect and Chandra X-ray measurements of high-redshift galaxy clusters |journal=[[The Astrophysical Journal]] |volume=647 |issue= 1|article-number=25 |arxiv=astro-ph/0512349 |bibcode=2006ApJ...647...25B |doi=10.1086/505291
 |s2cid=15723115
}}</ref>
| Combined [[Sunyaev–Zeldovich effect]] and Chandra X-ray observations of [[galaxy cluster]]s. Adjusted uncertainty in table from Planck Collaboration 2013.<ref name="planck2013_parameters">{{cite journal |author1=Planck Collaboration |date=2013 |title=Planck 2013 results. XVI. Cosmological parameters |arxiv=1303.5076 |doi=10.1051/0004-6361/201321591 |volume=571 |journal=Astronomy & Astrophysics |page=A16 |bibcode=2014A&A...571A..16P|s2cid=118349591 }}</ref>
|-
|2003
|{{val|72|5}}
|WMAP (First year) only
|<ref>{{Cite journal |last=Spergel |first=D.N. |date=September 2003 |title=First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters |url=https://iopscience.iop.org/article/10.1086/377226/meta |journal=The Astrophysical Journal Supplement Series |volume=148 |issue=1 |pages=175–194|doi=10.1086/377226 |arxiv=astro-ph/0302209 |bibcode=2003ApJS..148..175S |s2cid=10794058 }}</ref>
|
|-
| 2001-05
| {{val|72|8}}
| [[Hubble Space Telescope#Key projects|Hubble Space Telescope Key Project]]
| <ref name="Freedman2001">{{cite journal |last=Freedman |first=W. L. |display-authors=etal |year=2001 |title=Final results from the Hubble Space Telescope Key Project to measure the Hubble constant |journal=[[The Astrophysical Journal]] |volume=553 |issue=1 |pages=47–72 |arxiv=astro-ph/0012376 |bibcode=2001ApJ...553...47F |doi=10.1086/320638 |s2cid=119097691 }}</ref>
| This project established the most precise optical determination, consistent with a measurement of {{math|''H''{{sub|0}}}} based upon Sunyaev–Zel'dovich effect observations of many galaxy clusters having a similar accuracy.
|-
|before 1996
| {{val|50}} &mdash; {{val|90}} (est.)
|
| <ref name="Overbye">{{cite book |last=Overbye |first=D. |date=1999 |chapter=Prologue |title=Lonely Hearts of the Cosmos |page=1''ff'' |edition=2nd |publisher=[[HarperCollins]] |isbn=978-0-316-64896-7 }}</ref>
|
|-
|1994
|{{val|67|7}}
|Supernova 1a Light Curve Shapes
|<ref>{{Cite journal |last=Riess |first=Adam G. |date=January 1995 |title=Using SN Ia Light Curve Shapes to Measure The Hubble Constant |journal=[[The Astrophysical Journal]] |volume=438 |issue=L17|doi=10.1086/187704 |arxiv=astro-ph/9410054 |bibcode=1995ApJ...438L..17R |s2cid=118938423 }}</ref>
|Determined relationship between luminosity of SN 1a's and their Light Curve Shapes. Riess et al. used this ratio of the light curve of SN 1972E and the Cepheid distance to NGC 5253 to determine the constant.
|-
|mid 1970's
|{{val|100|10}}
|[[Gérard de Vaucouleurs]]
|<ref name=":0" />
|[[Gérard de Vaucouleurs|De Vaucouleurs]] believed he had improved the accuracy of Hubble's constant from Sandage's because he used 5x more primary indicators, 10× more calibration methods, 2× more secondary indicators, and 3× as many galaxy data points to derive his {{val|100|10}}.
|-
| early 1970s
| {{val|55}} (est.)
| Allan Sandage and [[Gustav Andreas Tammann|Gustav Tammann]]
| <ref name="cfa"/>
|
|-
| 1958
| {{val|75}} (est.)
| [[Allan Sandage]]
| <ref>{{cite journal |last=Sandage |first=A. R. |title=Current problems in the extragalactic distance scale |date=1958 |journal=[[The Astrophysical Journal]] |volume=127 |issue=3 |pages=513–526 |bibcode=1958ApJ...127..513S |doi=10.1086/146483 }}</ref>
| This was the first good estimate of {{math|''H''{{sub|0}}}}, but it would be decades before a consensus was achieved.
|-
| 1956
| {{val|180}}
| [[Milton L. Humason|Humason]], [[Nicholas Mayall|Mayall]] and Sandage
|<ref name="cfa">{{cite web |url=https://www.cfa.harvard.edu/~dfabricant/huchra/hubble |title=The Hubble Constant |author=John P. Huchra |website=Harvard Center for Astrophysics |date=2008 }}</ref>
|
|-
| 1929
| {{val|500}}
| [[Edwin Hubble]], [[Hooker telescope]]
|<ref>Edwin Hubble, ''A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae'', Proceedings of the National Academy of Sciences, vol. 15, no. 3, pp. 168-173, March 1929</ref><ref name="cfa"/><ref name="wwu">{{cite web |title=Hubble's Constant |url=https://www.wwu.edu/depts/skywise/hubble_constant.html |website=Skywise Unlimited – Western Washington University}}</ref>
|
|-
| 1927
| {{val|625}}
| [[Georges Lemaître]]
|<ref>{{cite journal|first=Georges|last=Lemaître|title=Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques|journal=Annales de la Société Scientifique de Bruxelles|volume=A47|pages=49–59|date=1927|bibcode=1927ASSB...47...49L|language=fr}}</ref>
|First measurement and interpretation as a sign of the [[expansion of the universe]].
|}

== See also ==
* {{Annotated link|List of scientists whose names are used in physical constants}}
* [[Lambda-CDM_model#S8_tension|S8 tension]]- a similar problem from another parameter of the ΛCDM model.
* {{Annotated link|Tests of general relativity}}

== Notes==
{{notelist}}

== References ==
{{reflist}}

=== Bibliography ===
* {{Cite book
 |last=Hubble |first=E. P.
 |date=1937
 |title=The Observational Approach to Cosmology
 |publisher=[[Clarendon Press]]
 |lccn=38011865
}}
* {{Cite book
 |last=Kutner
 |first=M.
 |date=2003
 |title=Astronomy: A Physical Perspective
 |publisher=Cambridge University Press
 |isbn=978-0-521-52927-3
 |url-access=registration
 |url=https://archive.org/details/astronomyphysica00kutn
}}
* {{Cite book
 |last=Liddle |first=A. R.
 |date=2003
 |title=An Introduction to Modern Cosmology
 |edition=2nd
 |publisher=[[John Wiley & Sons]]
 |isbn=978-0-470-84835-7
}}

== External links ==
* [http://map.gsfc.nasa.gov/universe/bb_tests_exp.html NASA's WMAP B ig Bang Expansion: the Hubble Constant]
* [http://www.ipac.caltech.edu/H0kp/H0KeyProj.html The Hubble Key Project]
* [http://cas.sdss.org/dr3/en/proj/advanced/hubble/ The Hubble Diagram Project]
* [https://www.forbes.com/sites/startswithabang/2019/05/03/cosmologys-biggest-conundrum-is-a-clue-not-a-controversy/ Coming to terms with different Hubble Constants] ([[Forbes]]; 3 May 2019)
* {{cite web|last=Merrifield|first=Michael|title=Hubble Constant|url=http://www.sixtysymbols.com/videos/hubble.htm|website=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|date=2009}}

{{Portal bar|Astronomy|Stars|Outer space}}

{{DEFAULTSORT:Hubble's Law}}
[[Category:Edwin Hubble|Law]]
[[Category:Eponymous laws of physics]]
[[Category:Large-scale structure of the cosmos]]
[[Category:Physical cosmology]]
[[Category:Equations of astronomy]]