Stable cosmological models driven by a free quantum scalar field

TL;DR

This paper rigorously analyzes semiclassical Einstein's equations with a quantum scalar field, demonstrating stable de Sitter-like solutions without a cosmological constant through algebraic quantum field theory methods.

Contribution

It provides a mathematically rigorous approach to semiclassical gravity with a quantum scalar field, showing stable, de Sitter-like solutions emerging naturally without a cosmological constant.

Findings

De Sitter type behavior in solutions without a cosmological constant

Stability of these semiclassical solutions

Rigorous algebraic quantum field theoretical framework

Abstract

In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling with gravity in the hypothesis that the underlying algebraic quantum state is of Hadamard type. Particularly, if we focus on highly symmetric solutions of the semiclassical Einstein's equations, the envisaged method displays a de Sitter type behaviour even without an a priori introduced cosmological constant. As a further novel result we shall show that these solutions turn out to be stable.