Finite Temperature Effective Potential for Gauge Models in de Sitter Space

TL;DR

This paper computes the finite-temperature one-loop effective potential for gauge models in de Sitter space, revealing phase transition behaviors and symmetry restoration phenomena influenced by the background space's radius.

Contribution

It introduces a relation linking gauge and scalar effective potentials at all temperatures and analyzes phase transitions in de Sitter space for the first time.

Findings

Effective potentials for gauge and scalar fields are related at all temperatures.

Symmetry restoration occurs at a critical de Sitter radius for broken gauge symmetries.

Phase transitions are identified as first or second order depending on the radius regime.

Abstract

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.