Global stability of the open Milne spacetime

TL;DR

This paper proves the global nonlinear stability of the open Milne spacetime under Einstein-scalar field equations, showing that the spacetime asymptotically approaches hyperbolic geometry over time.

Contribution

It establishes the first rigorous proof of the nonlinear stability of open Milne spacetime for both massive and massless scalar fields.

Findings

Spacetime remains stable under small perturbations.

The spatial metric converges to hyperbolic metric asymptotically.

Decay rates are derived using Gaussian normal coordinates.

Abstract

The open Milne cosmological spacetime has a 3-dimensional Cauchy surface isometric to the (non-compact) hyperbolic space. We prove the globally nonlinear stability of the open Milne spacetime for both massive and massless Einstein-scalar field equations and show that as time goes to infinity, the spatial metric tends to the hyperbolic metric. The proof is based on the Gaussian normal coordinates, in which the decay rates of gravity are determined by the expanding geometry of Milne spacetime.