  The one-loop effective potential for gauge models in static de Sitter space
at finite temperatures is computed by means of the $\zeta$--function method. We
found a simple relation which links the effective potentials of gauge and
scalar fields at all temperatures.
  In the de Sitter invariant and zero-temperature states the potential for the
scalar electrodynamics is explicitly obtained, and its properties in these two
vacua are compared. In this theory the two states are shown to behave similarly
in the regimes of very large and very small radii a of the background space.
For the gauge symmetry broken in the flat limit ($a \to \infty$) there is a
critical value of a for which the symmetry is restored in both quantum states.
Moreover, the phase transitions which occur at large or at small a are of the
first or of the second order, respectively, regardless the vacuum considered.
The analytical and numerical analysis of the critical parameters of the above
theory is performed. We also established a class of models for which the kind
of phase transition occurring depends on the choice of the vacuum.
