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A recent arXiv paper by Capozziello et al (27 Feb 2023) claims:

the H0 tension is not due to neither systematic errors, nor to some new physics beyond the $\Lambda$CDM model, but simply to the fact that, in measuring the same quantity at different redshift, different results arise thanks to the look-back time evaluated at different epochs.

Now, maybe the solution is really this "simple", and I might be missing something, but I thought the age of the universe/lookback times depend on input cosmological parameters, including the Hubble parameter, i.e., just the redshift isn’t enough. I am noting this paper claims the age of the universe by Planck collaboration was derived without using $H_0$ via six independent parameters.

How can the Capozziello et al claim stack up?

It would seem to me to be a reheated version of this claim by the same author.

Peter Mortensen
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Mr Anderson
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3 Answers3

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Their equation (5) says

$$T_{lt} = T_0 − T(z) = T_0 − a(t)T_0$$

where $T_{lt}$ is the light travel time and $T_0$ is the present age of the universe. That implies they're assuming $T=a\,T_0$. In a footnote they say

The parametrization $T(z) = a(t)T_0$ is assumed as a label for the age of the Universe at a given redshift.

Fine, but you can't do that and also equate $T$ with the cosmological time, which they do.

They could be equated in a Milne cosmology, where $a\propto t$. It may be true that Milne cosmology is a better fit to this data, but Milne cosmology requires either $Ω\approx 0$, which is strongly excluded by other data, or general relativity being wrong. The paper claims to resolve the tension within the standard ΛCDM model, so it's just wrong.

benrg
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While benrg would seem to be on the right track with the answer, just after this question was posted, there seems to have been professional interest as well, such that a Comment on: paper was put up on arXiv by Escamilla-Rivera et al (3rd March 2023). The comment papers two main conclusions, respectively:

The lookback approach...cannot address the $H_0$ tension completely. Recovering the values from current collaborations under this approach does not correspond to an answer on why such an issue could be associated with $z$ measurements; and

The circularity problem is not avoided entirely, since the age of the Universe is sensitive to both $\Omega_m$ and $H_0$ for a flat $\Lambda$CDM cosmology. However, the local determination of H0 is not sensitive to $\Omega_m$.

The comment on paper has now been withdrawn, so obviously something wrong. However, since most of the citations on Capozziello paper are self-citations by the authors, and nobody seems to be taking any notice of it, benrg is no doubt correct in any case.

Peter Mortensen
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Mr Anderson
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Look back time also known as light-travel distance isn't well defined, so it doesn't make sense to use it for astronomical calculations.

For more information please see Edward Wright's Article https://astro.ucla.edu/~wright/Dltt_is_Dumb.html I can't see these points discussed in the reference you show.

timm
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