Dynamical system approach to FRW models in higher-order gravity theories

Details Dynamical system approach to FRW models in higher-order gravity theories Dynamical system approach to FRW models in higher-order gravity theories

2003-05-16

arxiv.org/abs/gr-qc/0305062v1

J.Math.Phys. 44 (2003) 3900-3910

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 figures, to appear in JMP

Scientific paper

10.1063/1.1602161

We study the late time evolution of positively curved FRW models with a scalar field which arises in the conformal frame of the $R+\alpha R^{2}$ theory. The resulted three-dimensional dynamical system has two equilibrium solutions corresponding to a de Sitter space and an ever expanding closed universe. We analyze the structure of the first equilibrium with the methods of the center manifold theory and, for the second equilibrium we apply the normal form theory to obtain a simplified system, which we analyze with special phase plane methods. It is shown that an initially expanding closed FRW spacetime avoids recollapse.

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