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We consider a scenario where time dependence on physical parameters isintroduced by the misalignment of an ultra-light scalar field. The initial VEVof such field at the early time remains a constant until Hubble becomescomparable to its mass. Interesting cosmological consequences are considered.Light sterile neutrinos hinted by terrestrial neutrino experiments are studiedas a benchmark model. We show the BBN constraints can be easily avoided in thisscenario, even if reheating temperature is high. The scalar can be naturallylight in spite of its couplings to other fields. Parameters of sterile neutrinomay remain changing with time nowadays. This can further relax the tension fromthe recent IceCube constraints.

Cosmology and time dependent parameters induced by misaligned light scalar