Newtonian cosmology from quantum corrected Newtonian potential

TL;DR

This paper explores how quantum and classical corrections to Newtonian gravity influence cosmological models, deriving modified Friedmann equations and analyzing their effects on universe evolution with different matter contents.

Contribution

It introduces a derivation of modified Friedmann equations incorporating leading classical and quantum Newtonian potential corrections, highlighting the negligible impact of quantum corrections.

Findings

Quantum corrections are too small to affect physical results.

The universe's evolution is similar for radiation and dust at late times.

A bounce in the universe may occur depending on correction signs.

Abstract

We study the Newtonian cosmology taking into account the leading classical and quantum corrections of order $\mathcal{O}(G^{2})$ in the Newtonian potential. We first derive the modified Friedmann equations starting from the non-relativistic conservation of kinetic energy and potential energy for an infinitesimal mass. We then consider the leading classical correction term and the quantum correction term in the Newtonian potential for deriving the Friedmann equation, however, the quantum correction term is too small and hence does not contribute in the physical results. We then investigate the difference in scale factor with the usual scale factor for various matter like radiation, dust and cosmological constant by considering the corrections in the Newtonian potential. We observe that the evolution of the universe is similar for radiation and dust cases at late times. The cosmological constant case shows a steep increase in the scale factor compared to the other cases. We also note that the universe may have a bounce in the case of radiation depending on the sign of the coefficient of the leading classical correction.