  We consider an O(N) symmetric scalar field model in the mean field (Hartree)
approximation and show that the symmetry can be broken in de Sitter space. We
find that the phase transition can be of first order, and that its strength
depends non-analytically on the parameters of the model. We also show that the
would-be Goldstone bosons acquire a mass, effectively becoming pseudo-Goldstone
bosons, thus breaking the O(N) symmetry. Our results imply that topological
defects can form during inflation.
