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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.

MSC:
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
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