Thermodynamic stability in an Einstein universe

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 $\hat{I}¾$. By studying thermodynamics of massless scalar fields, we show that the only value of $\hat{I}¾$ 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.

22 pages, 6 figures. This version, except for stylistic changes, fits with the published version in PRD

Cited by in corpus (1)

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