Evolution of universes in quadratic theories of gravity

John D. Barrow and Sigbjørn Hervik
Phys. Rev. D 74, 124017 – Published 18 December 2006

Abstract

We use a dynamical systems approach to investigate Bianchi type I and II universes in quadratic theories of gravity. Because of the complicated nature of the equations of motion we focus on the stability of exact solutions and find that there exists an isotropic Friedmann-Robertson-Walker (FRW) universe acting as a past attractor. This may indicate that there is an isotropization mechanism at early times for these kind of theories. We also discuss the Kasner universes, elucidate the associated center manifold structure, and show that there exists a set of nonzero measure which has the Kasner solutions as a past attractor. Regarding the late-time behavior, the stability shows a dependence of the parameters of the theory. We give the conditions under which the de Sitter solution is stable and also show that for certain values of the parameters there is a possible late-time behavior with phantomlike behavior. New types of anisotropic inflationary behavior are found which do not have counterparts in general relativity.

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  • Received 3 October 2006

DOI:https://doi.org/10.1103/PhysRevD.74.124017

©2006 American Physical Society

Authors & Affiliations

John D. Barrow1,* and Sigbjørn Hervik2,†

  • 1DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Rd., Cambridge CB3 0WA, United Kingdom
  • 2Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

  • *Electronic address: J.D.Barrow@damtp.cam.ac.uk
  • Electronic address: herviks@mathstat.dal.ca

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Issue

Vol. 74, Iss. 12 — 15 December 2006

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