Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times

TL;DR

This paper investigates special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times, revealing solutions that resemble early universe radiation and late universe de Sitter expansion, with potential implications for the horizon problem.

Contribution

It introduces a numerical analysis of a fourth-order cosmological equation derived from semiclassical gravity with a massless scalar field, extending classical results to general coupling.

Findings

Discovery of a separation of quantum and scale factor dynamics

Identification of solutions resembling Big Bang and de Sitter expansion

Potential solution to the horizon problem through parameter tuning

Abstract

This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress-energy tensor of a quantum field with classical gravity. Here we consider a free massless scalar field with general (not necessarily conformal) coupling to curvature. In a cosmological scenario with flat spatial sections for special choices of the initial conditions, we observe a separation of the dynamics of the quantum degrees of freedom from the dynamics of the scale factor, which extends a classical result by Starobinsky to general coupling. For this new equation of fourth order for the dynamics of the scale factor, we study numerical solutions. Typical solutions show a radiation-like Big Bang for the early universe and de Sitter-like expansion for the late universe. We discuss a specific solution to the cosmological horizon problem that can be produced by tuning parameters in the given equation. Although the model proposed here only contains massless matter, we give a preliminary comparison of the obtained cosmology with the $\Lambda$CDM standard model of cosmology and investigate parameter ranges in which the new models to a certain extent assimilates standard cosmology.