Cosmological Newtonian limits on large spacetime scales

TL;DR

This paper proves the existence of solutions to Einstein-Euler equations with a positive cosmological constant that approximate Newtonian gravity on large scales, bridging relativistic and Newtonian cosmological models.

Contribution

It establishes the existence of parameter-dependent solutions that converge to Newtonian limits, providing a rigorous link between Einstein's equations and Newtonian cosmology.

Findings

Solutions exist globally and are future complete.

Solutions converge to cosmological Poisson-Euler equations as epsilon approaches zero.

Inhomogeneous perturbations evolve approximately according to Newtonian gravity.

Abstract

We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$, for the parameter values $0<\epsilon < \epsilon_0$. These solutions exist globally on the manifold $M=(0,1]\times \mathbb{R}^3$, are future complete, and converge as $\epsilon \searrow 0$ to solutions of the cosmological Poisson-Euler equations. They represent inhomogeneous, nonlinear perturbations of a FLRW fluid solution where the inhomogeneities are driven by localized matter fluctuations that evolve to good approximation according to Newtonian gravity.