Dark matter and nature of electroweak phase transition with an inert doublet

We provide a comprehensive and up-to-date analysis of the prospects to realize Dark Matter (DM) in the Inert Doublet Model, while simultaneously enhancing the Electroweak Phase Transition (EWPhT) such as to allow for electroweak baryogenesis. Instead of focusing on certain aspects or mass hierarchies, we perform extensive, yet fine-grained, parameter space scans, where we analyze the nature of the EWPhT in both the light and the heavy DM regions, confronting it with the amount of DM potentially residing in the lightest inert-doublet state. Thereby, we point out a viable region where a non-trivial two-step EWPhT can appear, without being in conflict with direct-detection bounds, which could leave interesting imprints in gravitational wave signatures. We propose new benchmarks with this feature as well as update benchmarks with a strong first-order transition in the light of new XENON1T limits. Moreover, taking into account these latest bounds as well as relevant collider constraints, we envisage a region for light DM with a small mass splitting, lifting the usual assumption of exact degeneracy of the new non-DM scalars, such as to avoid collider bounds while providing a fair DM abundance over a rather large DM mass range. This follows from a detailed survey of the impact of co-annihilations on the abundance, dissecting the various channels. (paper)