<p>The redshift scale-factor relationship might be different in an inhomogeneous universe or if General Relativity is incorrect.</p>
<p><a href="https://academic.oup.com/mnras/article/458/3/3331/2589357" rel="noreferrer">Wojtak &amp; Prada (2016)</a> test a one-parameter extension of the standard <span class="math-container">$\Lambda$</span>CDM model. They define <span class="math-container">$z_{\rm obs}$</span> as the observed redshift and <span class="math-container">$z$</span> as the redshift predicted by the FLRW metric and General Relativity <span class="math-container">$z = a^{-1} -1$</span>. The form they use is
<span class="math-container">$$
\frac{z}{z_{\rm obs}}=1+\frac{\alpha }{1+z_{\rm obs}},
$$</span>
such that the standard <span class="math-container">$z=z_{\rm obs}$</span> relation corresponds to <span class="math-container">$\alpha=0$</span>.</p>
<p>The authors test this model with Type Ia supernovae redshifts and distance estimates and with baryonic acoustic oscillation (BAO) measurements of Hubble parameters and angular distances.</p>
<p>They find that a joint analysis of the data is consistent with <span class="math-container">$\alpha =0$</span>, within the context of a <span class="math-container">$\Lambda$</span>CDM model.</p>
<p>However they show that the inclusion of high redshift Lyman alpha absorber BAO measurements favours <span class="math-container">$\alpha &gt; 0$</span> at 2 sigma significance.</p>
<p>Further, they point out that they can fit a CDM model (no dark energy) if <span class="math-container">$\alpha = -0.20 \pm 0.05$</span>.</p>
<p>A similar proposal was made by <a href="https://iopscience.iop.org/article/10.3847/1538-4357/aa86af" rel="noreferrer">Tian 2017</a>, who proposed tests using Type Ia supernovae, BAO data and the results from gravitational wave chirps with optical counterparts.</p>
<p>More recent revisitations of this idea as a means of removing the need for dark energy or the Hubble tension (at the expense of introducing a different fudge factor!) include <a href="https://app.dimensions.ai/details/publication/pub.1090167392" rel="noreferrer">Wojtak &amp; Prada (2017)</a> and <a href="https://link.springer.com/article/10.1007/s10509-024-04301-x" rel="noreferrer">Benedetto et al. (2024)</a>.</p>

CC BY-SA 4.0
2024-11-05T16:36:26.360Z
Thankyou, I'll have a good look at those links
John Hunter
CC BY-SA 4.0
2024-11-05T06:43:54.847Z
2024-11-05T07:54:11.837Z
2024-11-05T07:54:11.837Z
ProfRob
<p>The redshift scale-factor relation <span class="math-container">$a=\frac{1}{1+z}$</span> is derived from General Relativity and is fundamental to todays cosmological models.</p>
<p>However unlike all other predictions of General Relativity, e.g. the shift of the perihelion of Mercury, or gravitational time dilation, there seem to be no experimental tests - and therefore it could be incorrect.</p>
<p>The Concordance Cosmology, based on the above relation, has many problems, such as the Hubble tension, the unexplained nature of Dark Energy and observations of the James Webb telescope leading to the Impossible early galaxy problem.</p>
<p>Maybe the standard redshift - scale factor relationship is wrong.  Is there is any experimental evidence for it?</p>

CC BY-SA 4.0
2024-11-05T02:25:19.250Z
That falls out from GR overall, and GR overall makes predictions like the precession of Mercury. Trying to nitpick bits is not productive.
Jon Custer
CC BY-SA 4.0
2024-11-05T06:18:51.373Z
I think you'd get the same relation from an expanding Newtonian universe, (or from raisins in an expanding loaf of bread).  So it can't be used as a test of Relativity
James K
CC BY-SA 4.0
2024-11-05T08:52:18.580Z
@JonCuster  it's the 'falls out' attitude that's risky.  The relation has had no experimental test.  The question isn't nitpicking but about a serious suggestion about a possible way to deal with the difficulties cosmology is facing - a way that doesn't seem to have had much investigation
John Hunter
CC BY-SA 4.0
2024-11-05T08:54:14.000Z
@JamesK  General Relativity isn't in doubt, but the redshift scale-factor relation.   Until it's been tested, we can't be sure that we have used or interpreted GR correctly regarding the redshift of photons
John Hunter
CC BY-SA 4.0
2024-11-05T10:00:20.317Z
"The relation has had no experimental test." Are you asking this question in good faith?
ProfRob
CC BY-SA 4.0
2024-11-05T14:39:35.783Z
@ProfRob thankyou for the answer.  I'm suspicious that this relation is faulty and seems to have no experimental test, but I'd like to know other people's opinions in case there is a test that I haven't come across.
John Hunter
CC BY-SA 4.0
2024-11-05T17:04:12.457Z
The Wojtak & Prada (2017) paper presents detailed "redshift mapping" models constrained by data. They can solve many problems, but only by introducing at least 2 unexplained, new parameters $(z/z_{\rm obs})_0$ and some slope of how it varies in the past. I imagine if you allow more free parameters in $\Lambda$CDM (e.g. allow $\Lambda$ to change with time) you can also solve problems.
ProfRob
<cosmology><general-relativity><redshift>
What Experimental Evidence is there for the Redshift Scale-factor Relation?
John Hunter
# What Experimental Evidence is there for the Redshift Scale-factor Relation?

(Asked by: username_0 on 2024-11-04)

The redshift scale-factor relation $a=\frac{1}{1+z}$ is derived from General Relativity and is fundamental to todays cosmological models.

However unlike all other predictions of General Relativity, e.g. the shift of the perihelion of Mercury, or gravitational time dilation, there seem to be no experimental tests - and therefore it could be incorrect.

The Concordance Cosmology, based on the above relation, has many problems, such as the Hubble tension, the unexplained nature of Dark Energy and observations of the James Webb telescope leading to the Impossible early galaxy problem.

Maybe the standard redshift - scale factor relationship is wrong. Is there is any experimental evidence for it?

**Tags:** cosmology, general-relativity, redshift
> **Comments:**
> **username_1**: That falls out from GR overall, and GR overall makes predictions like the precession of Mercury. Trying to nitpick bits is not productive.  
> **username_2**: I think you'd get the same relation from an expanding Newtonian universe, (or from raisins in an expanding loaf of bread).  So it can't be used as a test of Relativity  
> **username_0**: @JonCuster  it's the 'falls out' attitude that's risky.  The relation has had no experimental test.  The question isn't nitpicking but about a serious suggestion about a possible way to deal with the difficulties cosmology is facing - a way that doesn't seem to have had much investigation  
> **username_0**: @JamesK  General Relativity isn't in doubt, but the redshift scale-factor relation.   Until it's been tested, we can't be sure that we have used or interpreted GR correctly regarding the redshift of photons  
> **username_3**: "The relation has had no experimental test." Are you asking this question in good faith?  
> **username_0**: @ProfRob thankyou for the answer.  I'm suspicious that this relation is faulty and seems to have no experimental test, but I'd like to know other people's opinions in case there is a test that I haven't come across.  
> **username_3**: The Wojtak & Prada (2017) paper presents detailed "redshift mapping" models constrained by data. They can solve many problems, but only by introducing at least 2 unexplained, new parameters $(z/z_{\rm obs})_0$ and some slope of how it varies in the past. I imagine if you allow more free parameters in $\Lambda$CDM (e.g. allow $\Lambda$ to change with time) you can also solve problems.  

---

## 1 answers

### Answer by username_3 on 2024-11-05. Score: 6 | Accepted answer

The redshift scale-factor relationship might be different in an inhomogeneous universe or if General Relativity is incorrect.

[Wojtak & Prada (2016)](https://academic.oup.com/mnras/article/458/3/3331/2589357) test a one-parameter extension of the standard $\Lambda$CDM model. They define $z\_{\rm obs}$ as the observed redshift and $z$ as the redshift predicted by the FLRW metric and General Relativity $z = a^{-1} -1$. The form they use is
$$
\frac{z}{z\_{\rm obs}}=1+\frac{\alpha }{1+z\_{\rm obs}},
$$
such that the standard $z=z\_{\rm obs}$ relation corresponds to $\alpha=0$.

The authors test this model with Type Ia supernovae redshifts and distance estimates and with baryonic acoustic oscillation (BAO) measurements of Hubble parameters and angular distances.

They find that a joint analysis of the data is consistent with $\alpha =0$, within the context of a $\Lambda$CDM model.

However they show that the inclusion of high redshift Lyman alpha absorber BAO measurements favours $\alpha > 0$ at 2 sigma significance.

Further, they point out that they can fit a CDM model (no dark energy) if $\alpha = -0.20 \pm 0.05$.

A similar proposal was made by [Tian 2017](https://iopscience.iop.org/article/10.3847/1538-4357/aa86af), who proposed tests using Type Ia supernovae, BAO data and the results from gravitational wave chirps with optical counterparts.

More recent revisitations of this idea as a means of removing the need for dark energy or the Hubble tension (at the expense of introducing a different fudge factor!) include [Wojtak & Prada (2017)](https://app.dimensions.ai/details/publication/pub.1090167392) and [Benedetto et al. (2024)](https://link.springer.com/article/10.1007/s10509-024-04301-x).

> **Comments:**
> **username_0**: Thankyou, I'll have a good look at those links  

---

