# Hypergeometrical Universe

## First Peer Review - 10

* 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. arXiv:1102.5278) and we would have know about such variations.

Answer: This was an interesting connection proposed by the Reviewer to challenge the epoch-dependent G.

I will tackle first the Oklo Natural Nuclear Reactor Argument. Oklo is 2 billion years old. During Oklo’s existence, G would had varied 1/13.58 to 1/11.58 or 13.58/11.58 = 117%. Gravitation would be 17% stronger. The effect of Gravitation would be felt as Gravitational dilation of time. If one considers two billion years as ${T}_{0}$ the dilation would be:

The effect of Gravity appears on the G terms. The largest contribution is of the order of 10^{-9}. If G is 17% stronger that term would still be irrelevant on the radioactive decay taking place in the Oklo cavern.

The fact that the depletion of Uranium is through a chain reaction process introduces a much higher uncertainty since through 2 billion years water levels in the cavern varied and thus the level of neutron moderation. I fail to see how epoch-dependent G could be detected by measurements in Oklo cavern.

Big Bang Nucleosynthesis had to consider not only an epoch-dependent G but also an epoch dependent Chandrasekhar mass (for Supernova Explosions) and an epoch dependent star size. Not only Chandrasekhar mass is dependent upon G but also the trigger mass of stars. Gas gathers in a star until it lights up. A stronger Gravity would make that process to happen at smaller masses. The stronger G means that internal pressure profile, luminosity would remain the same. The only thing different would be the average size of the star and the average lifetime of the star. We can only see a snapshot of any epoch, so we are not able to detect Star lifetime changes from epoch to epoch.

Nucleosynthesis is only sensitive to temperature and pressure profiles within stars and not their radiuses.

Smaller masses and stronger gravity would make celestial dynamics insensitive to G variations.

The referred article presents a model of screened Gravitation. Needless to say, their conclusions are model dependent and my interpretation of the Supernova Survey data challenges the 3D spacetime view. The other issue is that the article might not had considered that star masses would be smaller to compensate the increased Gravity.

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