Effective potential and Goldstone bosons in de Sitter space

Abstract

We investigate nonperturbative infrared effects for the O(N) linear sigma model in de Sitter space using the two-particle irreducible effective action at the Hartree truncation level. This approximation resums the infinite series of so-called superdaisy diagrams. For the proper treatment of ultraviolet divergences, we first study the renormalization of this approximation on a general curved background. Then, we calculate radiatively corrected masses and the effective potential. As a result, spontaneous symmetry breaking is possible, on the other hand, the Goldstone modes acquire a positive definite mass term due to the screening effects of interaction. Possible infrared divergence is self-regulated by the mass term. Furthermore, there is a symmetry restoring phase transition as a function of the Hubble parameter. In our approximation, the phase transition is of first order.