On the Asymptotic Stability of De-Sitter Spacetime: a non-linear perturbative approach

TL;DR

This paper proves that second-order perturbations of flat dust cosmological models decay over time, leading solutions to converge to De-Sitter spacetime, supporting the cosmic no-hair conjecture.

Contribution

It develops a non-linear perturbative framework for analyzing the asymptotic stability of De-Sitter spacetime including all perturbation modes.

Findings

Perturbations decay asymptotically in time.

Solutions converge to De-Sitter spacetime.

Results hold for arbitrary order perturbations.

Abstract

We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the perturbations decay asymptotically in time and that the solutions converge to the De-Sitter solution. By induction, this result is valid for perturbations of arbitrary order. This is in agreement with the cosmic no-hair conjecture of Gibbons and Hawking.