Dark Matter data and constraints on quartic couplings in IDM

We analyse the thermal evolution of the Universe in the Inert Doublet Model for three regions of Dark Matter masses: low mass (4-8) GeV, medium mass (30-80) GeV and high mass (500-1000) GeV. Those three regions of DM mass exhibit different behaviour, both in the possible types of evolution and in the energy relic density values. In this analysis we use the masses of the scalar particles as the input parameters to constrain the two self-couplings between neutral scalars: $\lambda_{345},\lambda_2$. These couplings are used to construct the parameter space where different types of evolution may be presented. We discuss the influence of the scalar masses on the type of the evolution. We also discuss the importance of the $\lambda_2$ self-coupling. We argue, that the astrophysical data along with the positivity constraints simultaneously constrain both $\lambda_{345}$ and $\lambda_2$ self-couplings.