Freeze-in dark matter via a light Dirac neutrino portal

We propose a scenario where dark matter (DM) can be generated nonthermally due to the presence of a light Dirac neutrino portal between the standard model (SM) and dark sector particles. The SM is minimally extended by three right-handed neutrinos (vR), a Dirac fermion DM candidate (yr) and a complex scalar (q), transforming nontrivially under an unbroken Z4 symmetry while being singlets under the SM gauge group. While DM and vR couplings are considered to be tiny in order to be in the nonthermal or freeze-in regime, q can be produced either thermally or nonthermally depending upon the strength of its Higgs portal coupling. We consider both these possibilities and find out the resulting DM abundance via freeze-in mechanism to constrain the model parameters in the light of Planck 2018 data. Since the interactions producing DM also produce relativistic vR, we check the enhanced contribution to the effective relativistic degrees of freedom Delta Neff in view of existing bounds as well as future sensitivities. We also check the stringent constraints on free-streaming length of such freeze-in DM from structure formation requirements. Such constraints can rule out DM mass all the way up to O(100 keV) keeping the Delta Neff <= O(10-3) out of reach from near future experiments. Possible extensions of this minimal model can lead to observable Delta Neff which can be probed at next generation experiments.