Freeze-in Dark Matter and $\Delta {\rm N}_{\rm eff}$ via Light Dirac
  Neutrino Portal
  We propose a scenario where dark matter (DM) and dark radiation ($\Delta {\rm
N}_{\rm eff}$) can be generated non-thermally 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
($\nu_R$), a Dirac fermion DM candidate ($\psi$) and a complex scalar ($\phi$),
transforming non-trivially under an unbroken $\mathbb{Z}_4$ symmetry while
being singlets under the SM gauge group. While DM and $\nu_R$ couplings are
considered to be tiny in order to be in the non-thermal or freeze-in regime,
$\phi$ can be produced either thermally or non-thermally depending upon the
strength of its Higgs portal coupling. We consider both these possibilities and
find out the resulting DM abundance and $\Delta {\rm N}_{\rm eff}$ via
freeze-in mechanism to constrain the model parameters in the light of Planck
2018 data. We find that the scenario where $\phi$ remains out of equilibrium
throughout or after a certain epoch allows more parameter space consistent with
DM phenomenology and $\Delta {\rm N}_{\rm eff}$ in view of Planck 2018 data.
The next generation experiments like CMB-S4, SPT-3G etc. will have the required
sensitivities to probe a major portion of the entire model parameter space,
offering a promising way of probing such non-thermal DM scenario which typical
direct detection experiments are not much sensitive to.
