The recollapse problem of closed FRW models in higher-order gravity theories

Details The recollapse problem of closed FRW models in higher-order gravity theories The recollapse problem of closed FRW models in higher-order gravity theories

2005-05-27

arxiv.org/abs/gr-qc/0505139v1

J.Math.Phys. 46 (2005) 082502

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 3 figures, submitted to JMP

Scientific paper

10.1063/1.2009648

We study the closed universe recollapse conjecture for positively curved FRW models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the $R+\alpha R^{2}$ theory. By including ordinary matter, we extend the analysis of a previous work. We analyze the structure of the resulted four-dimensional dynamical system with the methods of the center manifold theory and the normal form theory. It is shown that an initially expanding closed FRW universe, starting close to the Minkowski spacetime, cannot avoid recollapse. We discuss the posibility that potentials with a positive minimum may prevent the recollapse of closed universes.

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