Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-06-18
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages. Major changes to the original submission. Added discussion of power-law solutions
Scientific paper
A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the Einstein-Euler system. The resulting evolution system is used to show that, for some classes of scalar field potentials, small nonlinear perturbations of an expanding Friedmann-Robertson-Walker background with a selfinteracting scalar field source, decay exponentially to zero or converge to constant values. As an application of our results we discuss the nonlinear stability of flat power-law solutions produced by an exponential potential. It is found that for a certain range of the parameter $p$, there is stability even in the absence of accelerated expansion.
Alho Artur
Mena Filipe C.
Valiente Kroon Juan A.
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