Radiatively induced spontaneous symmetry breaking and phase transitions in curved spacetime

Abstract

Local gauge symmetries which are spontaneously broken in flat spacetime are shown to be restored for large spacetime curvatures. The case of symmetry breaking due to radiative quantum corrections in gauge theories with elementary scalar fields is considered explicitly. In spacetimes with a positive Ricci curvature scalar R and a cosmological event horizon, the critical curvature R C is of O( m H 2) or O( m W 2), depending on whether the theory is formulated with conformal or minimal scalar fields. In Ricci flat spacetimes with a conventional event horizon the symmetry is expected to be restored when the temperature of the Hawking thermal radiation is of O( m W). This phenomenon is described in detail, using functional integral methods and dimensional renormalization, for massless scalar electro-dynamics in de-Sitter spacetime. For conformal scalars, the symmetry restoring phase transition is first order, the critical curvature being R C = 0.910 m H 2. For minimal scalars, an anomalous, curvature dependent mass counterterm is required. The phase transition in this case is second order, and occurs at R C = 83.57 m W 2. Symmetry restoration at finite temperature in flat spacetime is considered in an appendix. The critical temperature at which a first-order phase transition occurs in the Weinberg-Salam model is found to be T C = 0.329 m W.