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 $\xi$. 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.

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

References in corpus (8)

• Casimir energy and a cosmological bounce
• Entropy Bounds in $R\times S^3$ Geometries
• Entropy bounds for massive scalar field in positive curvature space
• Hot scalar radiation setting bounds on the curvature coupling parameter
• Finite-temperature scalar fields and the cosmological constant in an Einstein universe
• Hot scalar radiation around a cosmic string setting bounds on the coupling parameter $\xi$
• Thermal fluctuations of a quantized massive scalar field in Rindler background
• Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes

Cited by in corpus (1)

• Accelerated expansion of the universe purely driven by scalar field fluctuations