Cosmological imprints of Dirac neutrinos in a keV-vacuum 2HDM

The Dirac neutrino masses could be simply generated by a neutrinophilic scalar doublet with a vacuum being dramatically different from the electroweak one. While the case with an eV-scale vacuum has been widely explored previously, we exploit in this work the desert where the scalar vacuum is of \begin{document}$\mathcal{O}(\mathrm{keV})$\end{document} scale. In this regime, there would be rare hope to probe the keV-vacuum neutrinophilic scalar model via the lepton-flavor-violating processes, which makes it distinguishable from the widely considered eV-scale vacuum. Although such a keV-vacuum scenario is inert in the low-energy flavor physics, we show that the baryogenesis realized via the lightest Dirac neutrino can be a natural candidate in explaining the baryon asymmetry of the Universe. Furthermore, the Dirac neutrinos with a keV-vacuum scalar can generate a shift of the effective neutrino number within the range \begin{document}$0.097\leqslant \Delta N_{\rm eff}\leqslant 0.112$\end{document}, which can be probed by the future Simons Observatory experiments. In particular, the model with a minimal value \begin{document}$\Delta N_{\rm eff}=0.097$\end{document} can already be falsified by the future CMB Stage-IV and Large Scale Structure surveys, providing consequently striking exploratory avenues in the cosmological regime for such a keV-vacuum scenario.