The non-linear asymptotic stability of De-Sitter: A perturbative approach

Abstract

We review recent results about the asymptotic decay of non-linear perturbations in cosmological models. We derive evolution and constraint equations for second order perturbations of flat L-dust Friedman-Lemaître-Robertson-Walker spacetimes using all scalar, vector and tensor perturbation modes. We show that the perturbations decay asymptotically in time and that the solutions converge to De-Sitter, in agreement with the cosmic no-hair conjecture. By induction, this result is valid for perturbations of any order.