  If the Dirac neutrino masses are generated by a new scalar doublet with a
vacuum at keV order, there would be rare hope to probe the framework in
low-energy flavor physics, such as the lepton-flavor violating processes.
However, the predicted neutrino Yukawa couplings being around the order of
electronic Yukawa can realize a purely thermal Dirac leptogenesis, and thus
render a more direct link between the high- and the low-energy CP violation.
Despite its inert property in the low-energy flavor processes, the keV-vacuum
induced Dirac neutrino model can generate a significant shift of the effective
neutrino number, which can in turn be probed by the big-bang nucleosynthesis
and cosmic microwave background epochs. We show that such a keV-vacuum induced
Dirac neutrino model is already constrained by the current observations and
will be probed with forecast sensitivity, serving therefore as a complementary
avenue to test the Dirac leptogenesis.
