Cosmic no-hair: non-linear asymptotic stability of de Sitter universe

TL;DR

This paper demonstrates that non-linear perturbations of de Sitter spacetime remain stable and tend to de Sitter values over time, supporting the cosmic no-hair conjecture even with inhomogeneous matter distributions.

Contribution

It extends the cosmic no-hair conjecture to non-linear inhomogeneous settings by analyzing second order perturbations in a dust-filled universe with a positive cosmological constant.

Findings

Non-linear perturbations tend to constants asymptotically.

Curvature invariants approach de Sitter values.

Geometry remains locally asymptotically de Sitter.

Abstract

We study the asymptotic stability of de Sitter spacetime with respect to non-linear perturbations, by considering second order perturbations of a flat Robertson-Walker universe with dust and a positive cosmological constant. Using the synchronous comoving gauge we find that, as in the case of linear perturbations, the non-linear perturbations also tend to constants, asymptotically in time. Analysing curvature and other spacetime invariants we show, however, that these quantities asymptotically tend to their de Sitter values, thus demonstrating that the geometry is indeed locally asymptotically de Sitter, despite the fact that matter inhomogeneities tend to constants in time. Our results support the inflationary picture of frozen amplitude matter perturbations that are stretched outside the horizon, and demonstrate the validity of the cosmic no-hair conjecture in the nonlinear inhomogeneous settings considered here.