Editing Cosmic microwave background (section)

==Theoretical models==
{{For|details about the reasoning that the radiation is evidence for the Big Bang|Big Bang#Cosmic microwave background radiation}}
The cosmic microwave background radiation and the [[Hubble's law|cosmological redshift]]-distance relation are together regarded as the best available evidence for the [[Big Bang]] event. Measurements of the CMB have made the inflationary Big Bang model the [[Standard Cosmological Model]].<ref>{{cite journal|last=Scott|first=D.|date=2005|title=The Standard Cosmological Model|arxiv=astro-ph/0510731|doi=10.1139/P06-066|volume=84|issue=6–7|journal=Canadian Journal of Physics|pages=419–435|bibcode = 2006CaJPh..84..419S |citeseerx=10.1.1.317.2954|s2cid=15606491}}</ref> The discovery of the CMB in the mid-1960s curtailed interest in [[non-standard cosmology|alternatives]] such as the [[steady state theory]].<ref>{{cite book|author=Durham, Frank|author2=Purrington, Robert D.|title=Frame of the universe: a history of physical cosmology|url=https://archive.org/details/frameofuniverseh0000durh|url-access=registration|publisher=Columbia University Press|date=1983|isbn=978-0-231-05393-8|pages=[https://archive.org/details/frameofuniverseh0000durh/page/193 193–209]}}</ref>

In the [[Big Bang]] model for the formation of the [[universe]], [[inflation (cosmology)|inflationary cosmology]] predicts that after about 10<sup>−37</sup> seconds<ref>{{cite book|last=Guth|first=A. H.|date=1998|title=The Inflationary Universe: The Quest for a New Theory of Cosmic Origins|page=[https://archive.org/details/inflationaryuniv0000guth/page/186 186]|publisher=[[Basic Books]]|isbn=978-0201328400|oclc=35701222|url=https://archive.org/details/inflationaryuniv0000guth/page/186}}</ref> the nascent universe underwent [[exponential growth]] that smoothed out nearly all irregularities. The remaining irregularities were caused by quantum fluctuations in the [[inflaton]] field that caused the inflation event.<ref>{{cite journal |last1=Cirigliano |first1=D. |last2=de Vega |first2=H.J. |last3=Sanchez |first3=N. G. |author-link3=Norma Sanchez |date=2005 |title=Clarifying inflation models: The precise inflationary potential from effective field theory and the WMAP data |url=https://cds.cern.ch/record/812888 |journal=[[Physical Review D]] |type=Submitted manuscript |volume=71 |issue=10 |pages=77–115 |arxiv=astro-ph/0412634 |bibcode=2005PhRvD..71j3518C |doi=10.1103/PhysRevD.71.103518 |s2cid=36572996}}</ref> Long before the formation of stars and planets, the early universe was more compact, much hotter and, starting 10<sup>−6</sup> seconds after the Big Bang, filled with a uniform glow from its white-hot fog of interacting [[Plasma (physics)|plasma]] of [[photon]]s, [[electron]]s, and [[baryon]]s.

As the universe [[metric expansion of space|expanded]], [[Adiabatic process|adiabatic]] cooling caused the energy density of the plasma to decrease until it became favorable for [[electron]]s to combine with [[proton]]s, forming [[hydrogen]] atoms. This [[recombination (cosmology)|recombination]] event happened when the temperature was around 3000&nbsp;K or when the universe was approximately 379,000&nbsp;years old.<ref>{{cite web|last=Abbott |first=B. |date=2007 |title=Microwave (WMAP) All-Sky Survey |url=http://www.haydenplanetarium.org/universe/duguide/exgg_wmap.php |publisher=[[Hayden Planetarium]] |access-date=2008-01-13 |url-status=dead |archive-url=https://web.archive.org/web/20130213023246/http://www.haydenplanetarium.org/universe/duguide/exgg_wmap.php |archive-date=2013-02-13 }}</ref> As photons did not interact with these electrically neutral atoms, the former began to travel [[free streaming|freely]] through space, resulting in the [[Decoupling (cosmology)|decoupling]] of matter and radiation.<ref>{{cite journal|last1=Gawiser|first1=E.|last2=Silk|first2=J.|date=2000|title=The cosmic microwave background radiation|journal=[[Physics Reports]]|volume=333–334|issue=2000|pages=245–267|doi=10.1016/S0370-1573(00)00025-9|arxiv=astro-ph/0002044|bibcode = 2000PhR...333..245G |citeseerx=10.1.1.588.3349|s2cid=15398837}}</ref>

The [[color temperature]] of the ensemble of decoupled photons has continued to diminish ever since; now down to {{val|2.7260|0.0013|u=K}},<ref name=apj707_2_916/> it will continue to drop as the universe expands. The intensity of the radiation corresponds to black-body radiation at 2.726&nbsp;K because red-shifted black-body radiation is just like black-body radiation at a lower temperature. According to the Big Bang model, the radiation from the sky we measure today comes from a spherical surface called ''the surface of last scattering''. This represents the set of locations in space at which the decoupling event is estimated to have occurred<ref>
{{cite web|last=Smoot|first=G. F.|date=2006|title=Cosmic Microwave Background Radiation Anisotropies: Their Discovery and Utilization|url=http://nobelprize.org/nobel_prizes/physics/laureates/2006/smoot-lecture.html|website=Nobel Lecture|publisher=[[Nobel Foundation]]|access-date=2008-12-22}}</ref><ref>{{cite web|url=https://map.gsfc.nasa.gov/media/990053/index.html|title=NASA's "CMB Surface of Last Scatter"|access-date=2023-07-05}}</ref> and at a point in time such that the photons from that distance have just reached observers. Most of the radiation energy in the universe is in the cosmic microwave background,<ref>{{cite book|last1=Hobson|first1=M.P.|last2=Efstathiou|first2=G.|last3=Lasenby|first3=A.N.|date=2006|title=General Relativity: An Introduction for Physicists|url=https://archive.org/details/generalrelativit00hobs_383|url-access=limited|pages=[https://archive.org/details/generalrelativit00hobs_383/page/n407 388]|publisher=[[Cambridge University Press]]|isbn=978-0-521-82951-9}}</ref> making up a fraction of roughly {{val|6|e=-5}} of the total density of the universe.<ref>{{cite book|last1=Unsöld|first1=A.|last2=Bodo|first2=B.|date=2002|title=The New Cosmos, An Introduction to Astronomy and Astrophysics|edition=5th|page=485|publisher=[[Springer-Verlag]]|isbn=978-3-540-67877-9|bibcode=2001ncia.book.....U}}</ref>

Two of the greatest successes of the Big Bang theory are its prediction of the almost perfect black body spectrum and its detailed prediction of the anisotropies in the cosmic microwave background. The CMB spectrum has become the most precisely measured black body spectrum in nature.<ref name="dpf99">
{{cite conference|last=White|first=M.|date=1999|title=Anisotropies in the CMB|book-title=Proceedings of the Los Angeles Meeting, DPF 99|publisher=[[UCLA]]|arxiv=astro-ph/9903232 |bibcode= 1999dpf..conf.....W }}</ref>

=== Predictions based on the Big Bang model ===

In the late 1940s Alpher and Herman reasoned that if there was a Big Bang, the expansion of the universe would have stretched the high-energy radiation of the very early universe into the microwave region of the [[electromagnetic spectrum]], and down to a temperature of about 5&nbsp;K. They were slightly off with their estimate, but they had the right idea. They predicted the CMB. It took another 15 years for Penzias and Wilson to discover that the microwave background was actually there.<ref name="Apeiron2_3_79"/>

According to standard cosmology, the CMB gives a snapshot of the hot early [[universe]] at the point in time when the temperature dropped enough to allow [[electron]]s and [[proton]]s to form [[hydrogen]] atoms. This event made the universe nearly transparent to radiation because light was no longer being [[Thomson scattering|scattered]] off free electrons.<ref>{{cite episode |last=Kaku |first=M. |author-link=Michio Kaku |date=2014 |title=First Second of the Big Bang |series=[[How the Universe Works]] |season=3 |number=4 |network=[[Science Channel|Discovery Science]]}}</ref> When this occurred some 380,000 years after the Big Bang, the temperature of the universe was about 3,000&nbsp;K. This corresponds to an ambient energy of about {{val|0.26|ul=eV}}, which is much less than the {{val|13.6|u=eV}} ionization energy of hydrogen.<ref>{{cite arXiv |eprint=astro-ph/9508159|last1=Fixsen|first1=D. J.|title=Formation of Structure in the Universe|year=1995}}</ref> This epoch is generally known as the "time of last scattering" or the period of [[recombination (cosmology)|recombination]] or [[Decoupling (cosmology)|decoupling]].<ref>{{cite web | url=https://physics.nist.gov/cgi-bin/cuu/Convert?exp=3&num=3&From=k&To=ev&Action=Convert+value+and+show+factor | title=Converted number: Conversion from K to eV}}</ref>

Since decoupling, the color temperature of the background radiation has dropped by an average factor of 1,089<ref name="FirstWMAP"/> due to the expansion of the universe. As the universe expands, the CMB photons are [[redshift]]ed, causing them to decrease in energy. The color temperature of this radiation stays [[inversely proportional]] to a parameter that describes the relative expansion of the universe over time, known as the [[scale factor (universe)|scale length]]. The color temperature ''T''<sub>r</sub> of the CMB as a function of redshift, ''z'', can be shown to be proportional to the color temperature of the CMB as observed in the present day (2.725&nbsp;K or 0.2348&nbsp;meV):<ref>{{cite journal | author=Noterdaeme, P. | author2=Petitjean, P. | author3=Srianand, R. | author4=Ledoux, C. | author5=López, S. | title=The evolution of the cosmic microwave background temperature. Measurements of T<sub>CMB</sub> at high redshift from carbon monoxide excitation | journal=Astronomy and Astrophysics | volume=526 |date=February 2011 | doi=10.1051/0004-6361/201016140 | bibcode=2011A&A...526L...7N | arxiv=1012.3164 | pages=L7 | s2cid=118485014 }}</ref>
:''T''<sub>r</sub> = 2.725&nbsp;K × (1 + ''z'')

The high degree of uniformity throughout the [[observable universe]] and its faint but measured anisotropy lend strong support for the Big Bang model in general and the [[Lambda-CDM model|ΛCDM ("Lambda Cold Dark Matter") model]] in particular. Moreover, the fluctuations are [[coherence (physics)|coherent]] on angular scales that are larger than the apparent [[cosmological horizon]] at recombination. Either such coherence is acausally [[fine-tuning (physics)|fine-tuned]], or [[cosmic inflation]] occurred.<ref name="hep-ph/0309057">{{cite journal |last=Dodelson |first=S. |year=2003 |title=Coherent Phase Argument for Inflation |journal=[[AIP Conference Proceedings]] |volume=689 |pages=184–196 |arxiv=hep-ph/0309057 |bibcode=2003AIPC..689..184D |doi=10.1063/1.1627736|citeseerx=10.1.1.344.3524 |s2cid=18570203 }}</ref><ref>{{Cite web |last=Baumann |first=D. |date=2011 |title=The Physics of Inflation |url=http://www.damtp.cam.ac.uk/user/db275/TEACHING/INFLATION/Lectures.pdf |publisher=[[University of Cambridge]] |access-date=2015-05-09 |archive-url=https://web.archive.org/web/20180921195002/http://www.damtp.cam.ac.uk/user/db275/TEACHING/INFLATION/Lectures.pdf |archive-date=2018-09-21 |url-status=dead }}</ref>

====Primary anisotropy====
[[File:PowerSpectrumExt.svg|thumb|right|300px|The power spectrum of the cosmic microwave background radiation temperature anisotropy in terms of the angular scale (or [[multipole moment]]). The data shown comes from the [[WMAP]] (2006), [[Arcminute Cosmology Bolometer Array Receiver|Acbar]] (2004) [[BOOMERanG experiment|Boomerang]] (2005), [[Cosmic Background Imager|CBI]] (2004), and [[Very Small Array|VSA]] (2004) instruments. Also shown is a theoretical model (solid line).]]
The [[anisotropy]], or directional dependency, of the cosmic microwave background is divided into two types: primary anisotropy, due to effects that occur at the surface of last scattering and before; and secondary anisotropy, due to effects such as interactions of the background radiation with intervening hot gas or gravitational potentials, which occur between the last scattering surface and the observer.

The structure of the cosmic microwave background anisotropies is principally determined by two effects: acoustic oscillations and [[diffusion damping]] (also called collisionless damping or [[Joseph Silk|Silk]] damping). The acoustic oscillations arise because of a conflict in the [[photon]]–[[baryon]] plasma in the early universe. The pressure of the photons tends to erase anisotropies, whereas the gravitational attraction of the baryons, moving at speeds much slower than light, makes them tend to collapse to form overdensities. These two effects compete to create acoustic oscillations, which give the microwave background its characteristic peak structure. The peaks correspond, roughly, to resonances in which the photons decouple when a particular mode is at its peak amplitude.

The peaks contain interesting physical signatures. The angular scale of the first peak determines the [[shape of the universe|curvature of the universe]] (but not the [[topology]] of the universe). The next peak—ratio of the odd peaks to the even peaks—determines the reduced baryon density.<ref>{{cite web |url=http://background.uchicago.edu/~whu/intermediate/baryons.html |title=Baryons and Inertia |author=Wayne Hu}}</ref> The third peak can be used to get information about the dark-matter density.<ref>{{cite web |url=http://background.uchicago.edu/~whu/intermediate/driving.html |title=Radiation Driving Force |author=Wayne Hu}}</ref>

The locations of the peaks give important information about the nature of the primordial density perturbations. There are two fundamental types of density perturbations called ''adiabatic'' and ''isocurvature''. A general density perturbation is a mixture of both, and different theories that purport to explain the primordial density perturbation spectrum predict different mixtures.
; Adiabatic density perturbations:In an adiabatic density perturbation, the fractional additional number density of each type of particle (baryons, [[photon]]s, etc.) is the same. That is, if at one place there is a 1% higher number density of baryons than average, then at that place there is a 1% higher number density of photons (and a 1% higher number density in neutrinos) than average. [[Cosmic inflation]] predicts that the primordial perturbations are adiabatic.
; Isocurvature density perturbations:In an isocurvature density perturbation, the sum (over different types of particle) of the fractional additional densities is zero. That is, a perturbation where at some spot there is 1% more energy in baryons than average, 1% more energy in photons than average, and 2% {{em|less}} energy in neutrinos than average, would be a pure isocurvature perturbation. Hypothetical [[cosmic string]]s would produce mostly isocurvature primordial perturbations.

The CMB spectrum can distinguish between these two because these two types of perturbations produce different peak locations. Isocurvature density perturbations produce a series of peaks whose angular scales (''ℓ'' values of the peaks) are roughly in the ratio 1&nbsp;:&nbsp;3&nbsp;:&nbsp;5&nbsp;:&nbsp;..., while adiabatic density perturbations produce peaks whose locations are in the ratio 1&nbsp;:&nbsp;2&nbsp;:&nbsp;3&nbsp;:&nbsp;...<ref name="hu_white_1996">{{cite journal|last1=Hu |first1=W.|last2=White|first2=M.|year=1996|title=Acoustic Signatures in the Cosmic Microwave Background|journal=[[Astrophysical Journal]]|volume=471|pages=30–51|doi=10.1086/177951|bibcode=1996ApJ...471...30H|arxiv = astro-ph/9602019 |s2cid=8791666}}</ref> Observations are consistent with the primordial density perturbations being entirely adiabatic, providing key support for inflation, and ruling out many models of structure formation involving, for example, cosmic strings.

Collisionless damping is caused by two effects, when the treatment of the primordial plasma as [[fluid]] begins to break down:
* the increasing [[mean free path]] of the photons as the primordial plasma becomes increasingly rarefied in an expanding universe,
* the finite depth of the last scattering surface (LSS), which causes the mean free path to increase rapidly during decoupling, even while some Compton scattering is still occurring.
These effects contribute about equally to the suppression of anisotropies at small scales and give rise to the characteristic exponential damping tail seen in the very small angular scale anisotropies.

The depth of the LSS refers to the fact that the decoupling of the photons and baryons does not happen instantaneously, but instead requires an appreciable fraction of the age of the universe up to that era. One method of quantifying how long this process took uses the ''photon visibility function'' (PVF). This function is defined so that, denoting the PVF by ''P''(''t''), the probability that a CMB photon last scattered between time ''t'' and {{nowrap|''t'' + ''dt''}} is given by ''P''(''t''){{thin space}}''dt''.

The maximum of the PVF (the time when it is most likely that a given CMB photon last scattered) is known quite precisely. The first-year [[Wilkinson Microwave Anisotropy Probe|WMAP]] results put the time at which ''P''(''t'') has a maximum as 372,000 years.<ref name="WMAP_1_cosmo_params">{{cite journal|author=WMAP Collaboration|year=2003|title=First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters|journal=[[Astrophysical Journal Supplement Series]]|volume=148|last2=Verde|issue=1|pages=175–194|first2=L.|doi=10.1086/377226|last3=Peiris|first3=H. V.|last4=Komatsu|first4=E.|last5=Nolta|first5=M. R.|last6=Bennett|first6=C. L.|last7=Halpern|first7=M.|last8=Hinshaw|first8=G.|last9=Jarosik|first9=N.|arxiv=astro-ph/0302209|bibcode=2003ApJS..148..175S|s2cid=10794058| display-authors = 8}}</ref> This is often taken as the "time" at which the CMB formed. However, to figure out how {{em|long}} it took the photons and baryons to decouple, we need a measure of the width of the PVF. The WMAP team finds that the PVF is greater than half of its maximal value (the "full width at half maximum", or FWHM) over an interval of 115,000 years.<ref name="WMAP_1_cosmo_params"/>{{rp|179}} By this measure, decoupling took place over roughly 115,000 years, and thus when it was complete, the universe was roughly 487,000 years old.

====Late time anisotropy====
Since the CMB came into existence, it has apparently been modified by several subsequent physical processes, which are collectively referred to as late-time anisotropy, or secondary anisotropy. When the CMB photons became free to travel unimpeded, ordinary matter in the universe was mostly in the form of neutral hydrogen and helium atoms. However, observations of galaxies today seem to indicate that most of the volume of the [[intergalactic medium]] (IGM) consists of ionized material (since there are few absorption lines due to hydrogen atoms). This implies a period of [[reionization]] during which some of the material of the universe was broken into hydrogen ions.

The CMB photons are scattered by free charges such as electrons that are not bound in atoms. In an ionized universe, such charged particles have been liberated from neutral atoms by ionizing (ultraviolet) radiation. Today these free charges are at sufficiently low density in most of the volume of the universe that they do not measurably affect the CMB. However, if the IGM was ionized at very early times when the universe was still denser, then there are two main effects on the CMB:
# Small scale anisotropies are erased. (Just as when looking at an object through fog, details of the object appear fuzzy.)
# The physics of how photons are scattered by free electrons ([[Thomson scattering]]) induces polarization anisotropies on large angular scales. This broad angle polarization is correlated with the broad angle temperature perturbation.

Both of these effects have been observed by the WMAP spacecraft, providing evidence that the universe was ionized at very early times, at a [[redshift]] around 10.<ref name="WMAP9Cosmo"/> The detailed provenance of this early ionizing radiation is still a matter of scientific debate. It may have included starlight from the very first population of stars ([[population III]] stars), supernovae when these first stars reached the end of their lives, or the ionizing radiation produced by the accretion disks of massive black holes.

The time following the emission of the cosmic microwave background—and before the observation of the first stars—is semi-humorously referred to by cosmologists as the [[Timeline of the Big Bang#Dark Ages|Dark Age]], and is a period which is under intense study by astronomers (see [[21 centimeter radiation]]).

Two other effects which occurred between reionization and our observations of the cosmic microwave background, and which appear to cause anisotropies, are the [[Sunyaev–Zeldovich effect]], where a cloud of high-energy electrons scatters the radiation, transferring some of its energy to the CMB photons, and the [[Sachs–Wolfe effect]], which causes photons from the Cosmic Microwave Background to be gravitationally redshifted or blueshifted due to changing gravitational fields.

===Alternative theories===
{{main| Non-standard cosmology }}
The standard cosmology that includes the Big Bang "enjoys considerable popularity among the practicing cosmologists"<ref name=NarlikarPadmanabhan>{{Cite journal |last1=Narlikar |first1=Jayant V. |last2=Padmanabhan |first2=T. |date=September 2001 |title=Standard Cosmology and Alternatives: A Critical Appraisal |url=https://www.annualreviews.org/doi/10.1146/annurev.astro.39.1.211 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=39 |issue=1 |pages=211–248 |doi=10.1146/annurev.astro.39.1.211 |bibcode=2001ARA&A..39..211N |issn=0066-4146}}</ref>{{rp|211}}
However, there are challenges to the standard big bang framework for explaining CMB data. In particular standard cosmology requires [[Fine-tuning (physics)|fine-tuning]] of some free parameters, with different values supported by different experimental data.<ref name=NarlikarPadmanabhan/>{{rp|245}}
As an example of the fine-tuning issue, standard cosmology cannot predict the present temperature of the relic radiation, <math>T_0</math>.<ref name=NarlikarPadmanabhan/>{{rp|229}} This value of <math>T_0</math> is one of the best results of experimental cosmology and the [[steady state model]] can predict it.<ref name="Apeiron2_3_79"/>
However, alternative models have their own set of problems and they have only made post-facto explanations of existing observations.<ref name=NarlikarPadmanabhan/>{{rp|239}} Nevertheless, these alternatives have played an important historic role in providing ideas for and challenges to the standard explanation.<ref name=HistoryOfAlternatives/>