Power-law Inflation in Spacetimes without Symmetry

TL;DR

This paper demonstrates the nonlinear stability of power-law inflationary solutions in Einstein-scalar field models without assuming symmetry, extending stability results to more general cosmological spacetimes.

Contribution

It proves the nonlinear stability of homogeneous and isotropic power-law inflation solutions without symmetry assumptions using advanced stability and reduction techniques.

Findings

Homogeneous and isotropic solutions are stable under small nonlinear perturbations.

Stability proof leverages nonlinear stability of de Sitter spacetime.

Kaluza-Klein reduction techniques are employed in the analysis.

Abstract

We consider models of accelerated cosmological expansion described by the Einstein equations coupled to a nonlinear scalar field with a suitable exponential potential. We show that homogeneous and isotropic solutions are stable under small nonlinear perturbations without any symmetry assumptions. Our proof is based on results on the nonlinear stability of de Sitter spacetime and Kaluza-Klein reduction techniques.