Massive sterile neutrinos in the early universe: From thermal decoupling to cosmological constraints

We consider relatively heavy neutrinos $ u_H$, mostly contributing to a sterile state $ u_s$, with mass in the range 10 MeV $lesssim m_s lesssim m_{pi} sim 135$ MeV, which are thermally produced in the early universe in collisional processes involving active neutrinos, and freezing out after the QCD phase transition. If these neutrinos decay after the active neutrino decoupling, they generate extra neutrino radiation, but also contribute to entropy production. Thus, they alter the value of the effective number of neutrino species $N_{rm eff}$ as for instance measured by the cosmic microwave background (CMB), as well as affect primordial nucleosynthesis (BBN), notably ${}^4$He production. We provide a detailed account of the solution of the relevant Boltzmann equations. We also identify the parameter space allowed by current Planck satellite data and forecast the parameter space probed by future Stage-4 ground-based CMB observations, expected to match or surpass BBN sensitivity.