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Inert Dark Matter and Strong Electroweak Phase Transition

The main virtue of the Inert Doublet Model (IDM) is that one of its spinless neutral bosons can play the role of Dark Matter. Assuming that the additional sources of CP violation are present in the form of higher dimensional operator(s) we reexamine the possibility that the model parameters for which the right number density of relic particles is predicted are compatible with the first order phase transition that could lead to electroweak baryogenesis. We find, taking into account recent indications from the LHC and the constraints from the electroweak precision data, that for a light DM (40-60 GeV) particle and heavy almost degenerate additional scalars $H^\pm$ and $A^0$ this is indeed possible but the two parameters most important for the strength of the phase transition: the common mass of $H^\pm$ and $A^0$ and the trilinear coupling of the Higgs-like particle to DM are strongly constrained. $H^\pm$ and $A^0$ must weight less than $\sim440$ GeV if the inert minimum is to be the lowest one and the value of the coupling is limited by the XENON 100 data. We stress the important role of the zero temperature part of the potential for the strength of the phase transition.