$\nu \Lambda$MDM: A Model for Sterile Neutrino and Dark Matter Reconciles Cosmological and Neutrino Oscillation Data after BICEP2

We propose a ultraviolet complete theory for cold dark matter(CDM) and sterile neutrino that can accommodate both cosmological data and neutrino oscillation experiments at $1\sigma$ level. A new $U(1)_X$ dark gauge symmetry is introduced, and is assumed to be broken at $\sim \mathcal{O}$(MeV) scale. Such a light mediator for DM's self-scattering and scattering-off sterile neutrinos can resolve three controversies for cold DM on small cosmological scales, cusp vs. core, too-big-to-fail and missing satellites problems. We can also accommodate $\sim$ eV scale sterile neutrinos as the hot dark matter(HDM) and can fit some neutrino anomalies from neutrino oscillation experiments within $1\sigma$. Finally the right amount of HDM can make a sizable contribution to dark radiation, and also helps to reconcile the tension between the data on the tensor-to-scalar ratio reported by Planck and BICEP2 Collaborations.