But putting all of that aside, I will take a narrow view of the manuscript. It proposes a distance(redshift) relation, and we can quantitatively see how well this matches the data. The proper way to do this is not by making plots, it is to compute chi^2 values from the distance moduli (mu) and covariance matrix in Union2.1:
chi^2 = (mu_observed - M - mu_theory)^T . (covariance matrix^-1) . (mu_observed - M - mu_theory)
where M is a constant that can be fit (the host-mass relation can also be fit, but failing to do so won’t affect the results much). After computing chi^2 values for LambdaCDM and HU, you can see if HU is favored or disfavored by the data compared to LambdaCDM. By my eye, HU is significantly worse, but the chi^2 values will say for sure.
I’m also skeptical that the luminosity of a SN Ia if G were different would scale as G^-3 (or M_ch^2).Read More
This manuscript presents the predicted luminosity distance in the Hypergeometrical Universe (HU) model and compares against the Union supernova compilation. Unfortunately, I do not believe that it is suitable for publication. I detail (only the major) issues below.Read More
So overall, I am not convinced that the author has properly calculated the actual impact of the geometry of the universe that he proposes. Since he is not modifying physics in a fundamental way, but only the geometry (which is arguably the appeal of his model), many experiments in physics can be reinterpreted in terms of this new setup. As far as I can tell, they would not allow the set up to be possible. Thus unless the author can convincingly prove that the standard well known local physics is not modified in his setup, it is premature to try to calculate the impact on cosmology.
* Finally, I do not think it is possible for G to vary in the way that the author proposes. For one, we have constraints on the variation of G on Earth from the Oklo natural nuclear reactor and, going back further into the past, from Big Bang Nucleosynthesis which mean that if cannot have change by more than a few percent. If it were changing together with Hubble, we would find that the galaxies and orbits destabilise etc. Moreover, as the author notices, stars are very sensitive to the strength of gravity (e.g.) and we would have know about such variations.Read More