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Shear dynamics in Bianchi I cosmologies with Rn-gravity

Jannie A Leach1, Sante Carloni1 and Peter K S Dunsby1,2

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We give the equations governing the shear evolution in Bianchi spacetimes for general f(R) theories of gravity. We consider the case of Rn-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approach a constant value.


PACS

98.80.Jk Mathematical and relativistic aspects of cosmology

04.50.-h Higher-dimensional gravity and other theories of gravity

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

MSC

83C15 Exact solutions

37D45 Strange attractors, chaotic dynamics

83F05 Cosmology

Subjects

Gravitation and cosmology

Statistical physics and nonlinear systems

Astrophysics and astroparticles

Dates

Issue 15 (7 August 2006)

Received 7 March 2006

Published 11 July 2006



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