Concealing Dirac neutrinos from cosmic microwave background

The existence of prolonged radiation domination prior to the Big Bang Nucleosynthesis (BBN), starting just after the inflationary epoch, is not yet established unanimously. If instead, the universe undergoes a non-standard cosmological phase, it will alter the Hubble expansion rate significantly and may also generate substantial entropy through non-adiabatic evolution. This leads to a thumping impact on the properties of relic species decoupled from the thermal bath before the revival of the standard radiation domination in the vicinity of the BBN. In this work, considering the Dirac nature of neutrinos, we have studied decoupling of ultra-relativistic right-handed neutrinos ($\nu_R$s) in presence of two possible non-standard cosmological phases. While in both cases we have modified Hubble parameters causing faster expansions in the early universe, one of the situations predicts a non-adiabatic evolution and thereby a slower redshift of the photon temperature due to the expansion. Considering the most general form of the collision term with Fermi-Dirac distribution and Pauli blocking factors, we have solved the Boltzmann equation numerically to obtain $\Delta{\rm N}_{\rm eff}$ for the three right-handed neutrinos. We have found that for a large portion of parameter space, the combined effect of early decoupling of $\nu_R$ as well as the slower redshift of photon bath can easily hide the signature of right-handed neutrinos, in spite of precise measurement of $\Delta{\rm N}_{\rm eff}$, at the next generation CMB experiments like CMB-S4, SPT-3G etc. This however will not be applicable for the scenarios with only fast expansion.