The semiclassical stability of de Sitter spacetime

TL;DR

This paper proves the semiclassical stability of de Sitter spacetime with a massive scalar field by analyzing small homogeneous deviations and solving the linearized backreaction problem, establishing the robustness of this cosmological solution.

Contribution

It develops a renormalization scheme and analytically solves the linearized stability problem for de Sitter spacetime with a scalar field, identifying only non-physical instabilities.

Findings

Stability of de Sitter spacetime under small homogeneous perturbations.

Analytical solution for the linearized backreaction problem.

Identification of artificial instabilities outside the semiclassical regime.

Abstract

de Sitter spacetime and Bunch-Davies vacuum are a solution to the semiclassical Einstein-Schroedinger equations describing the evolution of spacetime geometry and a massive scalar quantum field with arbitrary coupling to curvature. The stability of this solution is proven by calculating the renormalized energy momentum tensor expectation value for small spatially homogeneous deviations from the de Sitter - Bunch-Davies system and solving the linearized backreaction problem. A renormalization scheme is developed. All momentum integrations are carried out analytically. The general solution is given in terms of its Laplace transform. It contains only two artificial instabilities: a constant gauge mode and an instability on the Planck time scale lying outside of the scope of our semiclassical theory.