The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field Cosmologies (original) (raw)

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-perfect fluid system. The resulting evolution system is used to show that, for some classes of scalar field potentials, small non-linear perturbations of an expanding Klein-Gordon-Robertson-Walker background decay exponentially to zero or converge to constant values. * sequence is assumed to depend continously on the parameter ε in such a way that the limit ε → 0 renders the reference solutionů. In particular, one can write the full solution to the EFEs as the Ansatz