Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity

TL;DR

This paper explicitly solves semiclassical gravity equations for a de Sitter universe with a quantum scalar field, demonstrating the stability of de Sitter spacetime under isotropic perturbations and showing quantum effects slightly modify the cosmological constant.

Contribution

It provides an explicit solution for semiclassical gravity in a de Sitter universe and proves its stability under isotropic perturbations, independent of renormalization parameters.

Findings

Self-consistent de Sitter solution found with quantum scalar field

Quantum effects slightly shift the effective cosmological constant

De Sitter spacetime remains stable under isotropic perturbations

Abstract

A spatially flat Robertson-Walker spacetime driven by a cosmological constant is non-conformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially-isotropic perturbations of the metric and the quantum state. These results are independent of the free renormalization parameters.