Universal expansion with spatially varying $G$

Abstract

We calculate the expansion of the universe under the assumptions that $G$ varies in space and the radial size $r$ of the universe is very large (we call this the MOND regime of varying-$G$ gravity). The inferred asymptotic behavior turns out to be different than that found by McCrea & Milne in 1934 and our equations bear no resemblance to those of the relativistic case. In this cosmology, the scale factor $R(t)$ increases linearly with time $t$, the radial velocity is driven by inertia, and gravity is incapable of hindering the expansion. Yet, Hubble's law is borne out without any additional assumptions. When we include a repulsive acceleration $a_{\mathrm{de}}$ due to dark energy, the resulting universal expansion is then driven totally by this new term and the solutions for $a_{\mathrm{de}}\to 0$ do not reduce to those of the $a_{\mathrm{de}}\equiv 0$ case. This is a realization of a new Thom catastrophe: the inclusion of the new term destroys the conservation of energy and the results are not reducible to the previous case in which energy is conserved.

arXiv commentSubmitted to MNRASL. Matching the version considered for publication

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Cited by in corpus (3)

• Hints of Modified Gravity in Cosmos and in the Lab?
• Hubble tension vs two flows
• The modified Newton attraction law and its connection with cosmological $\Lambda$--term