TL;DR
This paper demonstrates that a broad class of inhomogeneous relativistic solutions can be accurately approximated by Newtonian gravity on cosmological scales, with error estimates confirming the validity of this approximation.
Contribution
It introduces a wide class of solutions showing Newtonian gravity can effectively approximate General Relativity in cosmology, with quantitative error bounds.
Findings
Newtonian solutions closely approximate relativistic ones on large scales
Error estimates quantify the difference between Newtonian and relativistic models
The results confirm Newtonian gravity's validity for cosmological simulations
Abstract
We describe a wide class of inhomogeneous relativistic solutions that are well approximated on cosmological scales by solutions of Newtonian gravity. Error estimates measuring the difference between the Newtonian and relativistic solutions are given. The solutions presented here unambiguously demonstrate that it is possible for Newtonian gravity to provide a good approximation to General Relativity on cosmological scales.
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