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 do not imply the existence of 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

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... ny finite N, however there is a first order phase transition as a function of the Hawking temperature T_H=H/2π. 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^2_π∝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_0c≃ 0.61 H/λ^1/4. In the strict N→∞ the symmetry cannot be spontaneously broken. Furthermore, the lack of kinematic thresholds imply that the Goldstone modes decay into Goldstone and Higgs modes by emission and absorption of superhorizon quanta.