Dark matter decaying into a Fermi sea of neutrinos

We study the possible decay of a coherently oscillating scalar field, interpreted as dark matter, into light fermions. Specifically, we consider a scalar field with sub-eV mass decaying into a Fermi sea of neutrinos. We recognize the similarity between our scenario and inflationary preheating where a coherently oscillating scalar field decays into standard model particles. Like the case of fermionic preheating, we find that Pauli blocking controls the dark matter decay into the neutrino sea. The radius of the Fermi sphere depends on the expansion of the universe leading to a time varying equation of state of dark matter. This makes the scenario very rich and we show that the decay rate might be different at different cosmological epochs. We categorize this in two interesting regimes and then study the cosmological perturbations to find the impact on structure formation. We find that the decay may help in alleviating some of the standard problems related to cold dark matter.