Spontaneous symmetry breaking in inflationary cosmology: on the fate of Goldstone Bosons

Daniel Boyanovsky

doi:10.1103/PhysRevD.86.023509

paper

Spontaneous symmetry breaking in inflationary cosmology: on the fate of Goldstone Bosons

arXiv:1205.3761 · doi:10.1103/PhysRevD.86.023509

Abstract

We argue that in an inflationary cosmology a consequence of the lack of time translational invariance is that spontaneous breaking of a continuous symmetry and Goldstone's theorem \emph{do not} imply the existence of \emph{massless} Goldstone modes. We study spontaneous symmetry breaking in an O(2) model, and implications for O(N) in de Sitter space time. The Goldstone mode acquires a radiatively generated mass as a consequence of infrared divergences, and the continuous symmetry is spontaneously broken for any finite $N$ , however there is a \emph{first order phase transition} as a function of the Hawking temperature $T_{H} = H /2 π$ . For O(2) the symmetry is spontaneously broken for $T_{H} < T_{c} = λ^{1/4} v /2.419$ where $λ$ is the quartic coupling and $v$ is the tree level vacuum expectation value and the Goldstone mode acquires a radiatively generated mass $M_{π}^{2} \propto λ^{1/4} H$ . The first order nature of the transition is a consequence of the strong infrared behavior of minimally coupled scalar fields in de Sitter space time, the jump in the order parameter at $T_{H} = T_{c}$ is $σ_{0 c} ≃ 0.61 H / λ^{1/4}$ . In the strict $N \to \infty$ the symmetry cannot be spontaneously broken. Furthermore, the lack of kinematic thresholds imply that the Goldstone modes \emph{decay} into Goldstone and Higgs modes by emission and absorption of superhorizon quanta.

arXiv comment32 pages, 6 figures

Spontaneous symmetry breaking in inflationary cosmology: on the fate of Goldstone Bosons

Abstract

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