A rigorous formulation of the cosmological Newtonian limit without averaging

TL;DR

This paper rigorously demonstrates the existence of cosmological solutions to Einstein-Euler equations that have a Newtonian limit without relying on averaging, including models with multiple fluid bodies.

Contribution

It introduces a class of exact cosmological solutions with Newtonian limits that do not depend on averaging procedures, expanding the understanding of the Newtonian limit in cosmology.

Findings

Proves existence of solutions with Newtonian limit

Includes models with finite number of fluid bodies

Solutions are exact and not based on averaging

Abstract

We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein-Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged.