A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies

TL;DR

This paper develops a conformal framework to analyze the non-linear stability of radiation-filled cosmological models, demonstrating their global existence and future completeness under perturbations.

Contribution

It introduces a conformal Einstein equation approach for tracefree fluids and proves the future stability of de Sitter-like radiation cosmologies.

Findings

Solutions are globally existent towards the future

Models are future geodesically complete

Stability results apply to de Sitter-like radiation cosmologies

Abstract

The conformal Einstein equations for a tracefree (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like tracefree (radiation) perfect fluid Friedman-Lema\^{\i}tre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete.