Nonlinear stability of the Milne model with matter

TL;DR

This paper proves that the Milne cosmological model remains stable under nonlinear perturbations when coupled with matter described by the Einstein-Vlasov system, using geometric and energy estimates.

Contribution

It establishes the nonlinear stability of the Milne model with matter, employing novel geometric L^2-estimates and a specific gauge choice for Einstein equations.

Findings

Milne model is future nonlinearly stable with matter

Uses geometric L^2-estimates for the distribution function

Employs constant-mean-curvature spatial harmonic gauge

Abstract

We show that any 3+1-dimensional Milne model is future nonlinearly, asymptotically stable in the set of solutions to the Einstein-Vlasov system. For the analysis of the Einstein equations we use the constant-mean-curvature-spatial-harmonic gauge. For the distribution function the proof makes use of geometric L^2-estimates based on the Sasaki-metric. The resulting estimates on the energy momentum tensor are then upgraded by employing the natural continuity equation for the energy density.