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The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field Cosmologies (1006.3778v4)
Published 18 Jun 2010 in gr-qc, math-ph, and math.MP
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-Lema^itre-Robertson-Walker backgrounds, with scalar field potentials satisfying certain future asymptotic conditions, decay exponentially to zero, in synchronous time.