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

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

2001-07-20

arxiv.org/abs/gr-qc/0107069v2

Class.Quant.Grav.19:L23-L29,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, REVTEX, submitted to Physical Review Letter

Scientific paper

10.1088/0264-9381/19/5/101

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.

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