Numerical Bianchi I solutions in semi-classical gravitation

TL;DR

This paper numerically investigates semi-classical Bianchi I cosmological solutions, demonstrating the emergence of physically relevant asymptotic states like de Sitter and Minkowski spaces due to quantum backreaction effects.

Contribution

It provides the first numerical solutions for semi-classical Einstein equations in Bianchi I spacetimes, highlighting the role of quantum backreaction in cosmological evolution.

Findings

Existence of physical solutions asymptotic to de Sitter and Minkowski spaces.

Identification of spurious solutions that are not physically relevant.

Quantum backreaction influences the late-time behavior of anisotropic universes.

Abstract

It is believed that soon after the Planck era, spacetime should have a semi-classical nature. In this context we consider quantum fields propagating in a classical gravitational field and study the backreaction of these fields, using the expected value of the energy-momentum tensor as source of the gravitational field. According to this theory, the escape from General Relativity theory is unavoidable. Two geometric counter-term are needed to regularize the divergences which come from the expected value. There is a parameter associated to each counter-term and in this work we found numerical solutions of this theory to particular initial conditions, for general Bianchi Type I spaces. We show that even though there are spurious solutions some of them can be considered physical. These physical solutions include de Sitter and Minkowski that are obtained asymptotically.