Inert Scalar Doublet Asymmetry as Origin of Dark Matter

In the inert scalar doublet framework, we analyze what would be the effect of a $B-L$ asymmetry that could have been produced in the Universe thermal bath at high temperature. We show that, unless the "$\lambda_5$" scalar interaction is tiny, this asymmetry is automatically reprocessed in part into an inert scalar asymmetry that could be at the origin of dark matter today. Along this scenario, the inert mass scale lies in the few-TeV range and direct detection constraints require that the inert scalar particles decay into a lighter dark matter particle which, as the inert doublet, is odd under a $Z_2$ symmetry.