Cosmology and time dependent parameters induced by misaligned light scalar

We consider a scenario where time dependence on certain physical parameters can be introduced by the misalignment of an ultra-light scalar field. The initial VEV of such field at the early Universe remains a constant until Hubble becomes comparable to its mass. Interesting cosmological consequences, such as modification of $N_{eff}$ or the dark matter (DM) relic abundance, are considered. Light sterile neutrinos implied by terrestrial neutrino experiments are studied as a benchmark model. We show the BBN constraints can be easily avoided in our scenario. We demonstrate the scalar can be naturally light in spite of its couplings to other fields.