Proof of the Cosmic No-Hair Conjecture for Quadratic Homogeneous Cosmologies

Details Proof of the Cosmic No-Hair Conjecture for Quadratic Homogeneous Cosmologies Proof of the Cosmic No-Hair Conjecture for Quadratic Homogeneous Cosmologies

1997-12-04

arxiv.org/abs/gr-qc/9712026v1

Class.Quant.Grav. 15 (1998) 2795-2801

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, LaTeX (IOP style), submitted to Class.Quant.Grav

Scientific paper

10.1088/0264-9381/15/9/024

We prove the cosmic no-hair conjecture for all orthogonal Bianchi cosmologies with matter in the $R+\beta R^2$ theory using the conformally equivalent Einstein field equations, with the scalar field having the full self-interacting potential, in the presence of the conformally related matter fields. We show, in particular, that the Bianchi IX universe asymptotically approaches de Sitter space provided that initially the scalar three-curvature does not exceed the potential of the scalar field associated with the conformal transformation. Our proof relies on rigorous estimates of the possible bounds of the so-called Moss-Sahni function which obeys certain differential inequalities and a non-trivial argument which connects the behaviour of that function to evolution of the spatial part of the scalar curvature.

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