Dynamical Backreaction in Robertson-Walker Spacetime

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 space time. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the sigularities 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.

Obtained equation of motion for non-conformal coupling, not just counter terms as in previous version. Typos fixed, renormalization term proportional to R added

References in corpus (4)

• Adiabatic vacuum states on general spacetime manifolds: Definition, construction, and physical properties
• Comments on the Stress-Energy Tensor Operator in Curved Spacetime
• Riemann Normal Coordinate expansions using Cadabra
• States of Low Energy on Robertson-Walker Spacetimes

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• The Chaplygin Gas Equation of State for the Quantized Free Scalar Field on Cosmological Spacetimes
• Energy conditions allow eternal inflation
• The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System
• The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor
• Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models