Back-reaction of Quantum fields in an Einstein Universe

TL;DR

This paper investigates how quantum fields at finite temperature influence the structure of an Einstein universe, revealing critical temperature-radius relations and phase transitions linked to Bose-Einstein condensation.

Contribution

It provides a novel analysis of back-reaction effects of quantum fields in an Einstein universe, establishing temperature-radius relations and phase transition points.

Findings

Existence of a minimum universe radius for self-consistent solutions.

Identification of a maximum temperature indicating a phase transition.

Connection between Bose-Einstein condensation and universe behavior.

Abstract

We study the back-reaction effects of the finite-temperature scalar field and the photon field in the background of an Einstein universe. In each case we find a relation between the temperature of the universe and its radius. These relations exhibit a minimum radius below which no self-consistent solution for the Einstein field equation can be found. A maximum temperature marks the transition from the vacuum dominated era to the radiation dominated era. An interpretation to this behavior in terms of Bose-Einstein condensation in the case of the scalar field is given.