Finite-temperature scalar field theory in static de Sitter space

The finite-temperature one-loop effective potential for a scalar field in static de Sitter space-time is obtained by using the $\zeta$-function method. Near the zero and Hawking temperatures, the de Sitter-invariant state, the effective potential is represented as a power-series expansion of the temperature, and its behavior is studied. The analysis shows the important role played by the curvature on the absolute minima of the potential. The effects of conical singularities of the space, appearing in the functional integral formalism for the thermal averages, are also discussed in connection with the scaling properties of the theory.