  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.
