Thermal Casimir effect in closed cosmological models with a cosmic string

Abstract

We consider the thermal corrections to the Casimir energy of a massless scalar field in the space-time with topology ${S}^{3}\ifmmode\times\else\texttimes\fi{}{R}^{1}$ (Einstein and Friedmann universes) containing an idealized cosmic string. The vacuum energy of the field under consideration, in this background, can be separated in two terms: one term that is simply the known vacuum energy of the massless scalar field in the Einstein and Friedmann cosmological models and the other term that formally corresponds to the vacuum energy of the electromagnetic field, also in the Einstein and Friedmann universes, multiplied by the cosmic string parameter $\ensuremath{\lambda}=(1/\ensuremath{\alpha})\ensuremath{-}1$, where $\ensuremath{\alpha}$ is a constant related to the cosmic string tension, $G\ensuremath{\mu}$. The Casimir free energy and all the other thermodynamic expressions can also be separated in the same way. Thus, we use the expressions calculated in previous works for the massless scalar and electromagnetic fields in the closed Einstein and Friedmann models to investigate the low- and high-temperature limits of the Casimir free energy, internal energy, and entropy and show the role played by the presence of a cosmic string.