Editing Hubble's law (section)

=== 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}}