Thermal Casimir effect for neutrino and electromagnetic fields in the closed Friedmann cosmological model

Abstract

We calculate the total internal energy, total energy density and pressure, and the free energy for the neutrino and electromagnetic fields in Einstein and closed Friedmann cosmological models. The Casimir contributions to all these quantities are separated. The asymptotic expressions for both the total internal energy and free energy, and for the Casimir contributions to them are found in the limiting cases of low and high temperatures. It is shown that the neutrino field does not possess a classical limit at high temperature. As for the electromagnetic field, we demonstrate that the total internal energy has the classical contribution and the Casimir internal energy goes to the classical limit at high temperature. The respective Casimir free energy contains both linear and logarithmic terms with respect to the temperature. The total and Casimir entropies for the neutrino and electromagnetic fields at low temperature are also calculated and shown to be in agreement with the Nernst heat theorem.