Intimate Relationship between Sterile Neutrino Dark Matter and ΔNeff

The self-interacting neutrino hypothesis is well motivated for addressing the tension between the origin of sterile neutrino dark matter and indirect detection constraints. It can also result in a number of testable signals from the laboratories to the cosmos. We show that, in a broad class of models, where the sterile neutrino dark matter relic density is generated by a light neutrinophilic mediator, there must be a lower bound on the amount of extra radiation in early Universe, in particular, ΔNeff > 0.12 at the cosmic microwave background (CMB) epoch. This lower bound will be further strengthened with an improved x-ray search at the Athena observatory. Such an intimate relationship will be unambiguously tested by the upcoming CMB Stage 4 project.