Thermodynamic stability in an Einstein universe

TL;DR

This paper investigates the thermodynamic stability of scalar fields in an Einstein universe, finding that conformal coupling ($\xi=1/6$) is necessary for stability across all conditions.

Contribution

It demonstrates that only conformally coupled scalar fields ensure thermodynamic stability in an Einstein universe at all temperatures and radii.

Findings

Conformal coupling ($\xi=1/6$) is required for stable thermodynamics.

Scalar blackbody radiation's properties depend on the curvature coupling parameter.

Presence of scalar fields is essential for stability alongside electromagnetic and neutrino radiation.

Abstract

We calculate the Feynman propagator at finite temperature in an Einstein universe for a neutral massive scalar field arbitrarily coupled to the Ricci curvature. Then, the propagator is used to determine the mean square fluctuation, the internal energy, and pressure of a scalar blackbody radiation as functions of the curvature coupling parameter $\xi$. By studying thermodynamics of massless scalar fields, we show that the only value of $\xi$ consistent with stable thermodynamic equilibrium at all temperatures and for all radii of the universe is $1/6$, i.e., corresponding to the conformal coupling. Moreover, if electromagnetic and neutrino radiations are present at the regime of high temperatures and/or large radii, we show that at least one scalar field must also be present to ensure thermodynamic stability.