zbMATH — the first resource for mathematics

The Einstein-Friedrich-nonlinear scalar field system and the stability of scalar field cosmologies. (English) Zbl 1386.83005
Summary: 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.

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
93C20 Control/observation systems governed by partial differential equations
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C47 Methods of quantum field theory in general relativity and gravitational theory
Full Text: DOI arXiv