The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field Cosmologies
arXiv:1006.3778
Abstract
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 small nonlinear perturbations of expanding Friedman-Lemaître-Robertson-Walker backgrounds, with scalar field potentials satisfying certain future asymptotic conditions, decay exponentially to zero, in synchronous time.
Version 4: Matches final published version