Linear stability of semiclassical theories of gravity

Abstract

The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model mimics also the evolution induced by semiclassical Einstein equations, such as the one which describes the early universe in the cosmological case. The equations governing the dynamics of linear perturbations around simple exact solutions of this toy model are analyzed by constructing the corresponding retarded fundamental solutions, and by discussing the corresponding initial value problem. It is shown that, if the quantum field which drives the back-reaction to the classical background is massive, then there are choices of the renormalization parameters for which the linear perturbations with compact spatial support decay polynomially in time for large times, thus indicating stability of the underlying semiclassical solution.

arXiv comment29 pages, 4 figures. Added some details about the perturbative construction. Changed part of Proposition 3.3. and added some details in the proof of Proposition 3.4. Added some references and made other minor corrections

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Cited by in corpus (5)

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• Quantum Field Theory in Curved Spacetime (2nd Edition)
• Cosmological de Sitter Solutions of the Semiclassical Einstein Equation
• The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor
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