**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.**

*** 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.**

**The rest of the paper in fact makes use of some simple geometrical arguments to obtain distances and I have to admit I do not understand what they refer to. Proper null geodesics of the metric must be calculated to be able to say anything about distances.**

*** I do not understand why the author uses the standard equation for luminosity distance in LambdaCDM cosmology (calling it the "improved Hubble law"). This fundamentally assume an FRW geometry in 3 spatial dimensions, with the cosmological constant and non-relativitistic matter as the only sources of energy in the universe. If the author would like to make claims about how well supernovae fit his model, he should start with a metric and with a definition of how light propagates (e.g. on null geodesics in standard physics). Given the metric and its dynamics which one would obtain by solving Einstein equations, an equation for the luminosity distance-redshift relation can be derived. It would be different.**

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