Casimir effect at nonzero temperature in closed Friedmann Universe

We investigate the finite-size effects upon the free energy of massive and massless scalar field with arbitrary coupling to gravity at nonzero temperature in a slowly evolving closed Friedmann Universe. The renormalized free energy and the resulting energy density and pressure are found and their physical consequence are discussed. The equation of state turns out to have the form $P=\rho/3$ for radiation with arbitrary coupling.