Global Existence of Solutions of the Semiclassical Einstein Equation for Cosmological Spacetimes

Abstract

We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get a state for the quantum field which gives finite expectation values for the stress-energy tensor. Furthermore, it is possible to control this expectation value by means of a global estimate on regular cosmological spacetimes. The obtained estimates permit to write a theorem about the existence and uniqueness of the local solutions encompassing both the spacetime metric and the matter field simultaneously. Finally, we show that one can always extend local solutions up to a point where the scale factor becomes singular or the Hubble function reaches a critical value $H_c=180\pi /G$, which both correspond to a divergence of the scalar curvature, namely a spacetime singularity.

20 pages; corrected references

References in corpus (7)

• Stable cosmological models driven by a free quantum scalar field
• On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornification
• Cosmological horizons and reconstruction of quantum field theories
• States of Low Energy on Robertson-Walker Spacetimes
• Wave Equations on Lorentzian Manifolds and Quantization
• On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications
• The Lambda CDM-model in quantum field theory on curved spacetime and Dark Radiation

Cited by in corpus (16)

• Backreaction in Cosmology
• Semiclassical theories as initial value problems
• A semiclassical singularity theorem
• Static symmetric solutions of the semi-classical Einstein-Klein-Gordon system
• On the initial value problem for semiclassical gravity without and with quantum state collapses
• Locally covariant quantum field theory with external sources
• Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times
• Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes
• Cosmological de Sitter Solutions of the Semiclassical Einstein Equation
• Linear stability of semiclassical theories of gravity
• The Semiclassical Einstein Equation on Cosmological Spacetimes
• The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System
• The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor
• Curvature fluctuations on asymptotically de Sitter spacetimes via the semiclassical Einstein's equations
• Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models
• Global Hyperbolicity and Self-adjointness