Closed cosmologies with a perfect fluid and a scalar field

Details Closed cosmologies with a perfect fluid and a scalar field Closed cosmologies with a perfect fluid and a scalar field

2000-04-19

arxiv.org/abs/gr-qc/0004060v1

Phys.Rev. D62 (2000) 043526

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 10 figures

Scientific paper

10.1103/PhysRevD.62.043526

Closed, spatially homogeneous cosmological models with a perfect fluid and a scalar field with exponential potential are investigated, using dynamical systems methods. First, we consider the closed Friedmann-Robertson-Walker models, discussing the global dynamics in detail. Next, we investigate Kantowski-Sachs models, for which the future and past attractors are determined. The global asymptotic behaviour of both the Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either expand from an initial singularity, reach a maximum expansion and thereafter recollapse to a final singularity (for all values of the potential parameter kappa), or else they expand forever towards a flat power-law inflationary solution (when kappa^2<2). As an illustration of the intermediate dynamical behaviour of the Kantowski-Sachs models, we examine the cases of no barotropic fluid, and of a massless scalar field in detail. We also briefly discuss Bianchi type IX models.

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