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DYNAMICAL BACKREACTION IN ROBERTSON–WALKER SPACETIME

BENJAMIN ELTZNER

Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany

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and

HANNO GOTTSCHALK

Bergische Universität Wuppertal, Fachgruppe Mathematik, Gaußstraße 20, D-42119 Wuppertal, Germany

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https://doi.org/10.1142/S0129055X11004357Cited by:17 (Source: Crossref)

Abstract

The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson–Walker spacetime. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the singularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson–Walker scale parameter a(t) coupled to the scalar field is finally derived for the case of conformal and also general coupling.

Keywords:

AMSC: 81T05

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