Planck-scale effects on global symmetries: Cosmology of pseudo-Goldstone bosons

We consider a model with a small explicit breaking of a global symmetry, as suggested by gravitational arguments. Our model has one scalar field transforming under a nonanomalous U(1) symmetry, and coupled to matter and to gauge bosons. The spontaneous breaking of the explicitly broken symmetry gives rise to a massive pseudo-Goldstone boson. We analyze thermal and nonthermal production of this particle in the early universe, and perform a systematic study of astrophysical and cosmological constraints on its properties. We find that for very suppressed explicit breaking the pseudo-Goldstone boson is a cold dark matter candidate.