Cosmology and time dependent parameters induced by misaligned light scalar
We consider a scenario where time dependence on physical parameters is introduced by the misalignment of an ultra-light scalar field. The initial VEV of such field at the early time remains a constant until Hubble becomes comparable to its mass. Interesting cosmological consequences are considered. Light sterile neutrinos hinted by terrestrial neutrino experiments are studied as a benchmark model. We show the BBN constraints can be easily avoided in this scenario, even if reheating temperature is high. The scalar can be naturally light in spite of its couplings to other fields. Parameters of sterile neutrino may remain changing with time nowadays. This can further relax the tension from the recent IceCube constraints.