Finite-temperature scalar fields and the cosmological constant in an Einstein universe

TL;DR

This paper investigates how finite-temperature massless scalar fields influence the Einstein universe's radius and cosmological constant, revealing a maximum temperature and notable differences based on coupling type.

Contribution

It introduces a detailed analysis of the back reaction effects of scalar fields at finite temperatures in an Einstein universe, highlighting differences between minimal and conformal coupling.

Findings

Existence of a maximum temperature below the Planck scale.

Significant differences in the cosmological constant between coupling types.

Relationship between universe radius and temperature derived.

Abstract

We study the back reaction effect of massless minimally coupled scalar field at finite temperatures in the background of Einstein universe. Substituting for the vacuum expectation value of the components of the energy-momentum tensor on the RHS of the Einstein equation, we deduce a relationship between the radius of the universe and its temperature. This relationship exhibit a maximum temperature, below the Planck scale, at which the system changes its behaviour drastically. The results are compared with the case of a conformally coupled field. An investigation into the values of the cosmological constant exhibit a remarkable difference between the conformally coupled case and the minimally coupled one.