The 2HD+a model: collider, dark matter and gravitational wave signals

We perform a comprehensive study of a model in which the Higgs sector is extended to contain two Higgs doublet fields, with the four types of possibilities to couple to standard fermions, as well as an additional light pseudoscalar Higgs boson which mixes with the one of the two doublets. This 2HD+a model includes also a stable isosinglet massive fermion that has the correct thermal relic abundance to account for the dark matter in the Universe. We summarize the theoretical constraints to which the model is subject and then perform a detailed study of the phenomenological constraints. In particular, we discuss the bounds from the LHC in the search for light and heavy scalar resonances and invisible states and those from high precision measurements in the Higgs, electroweak and flavor sectors, addressing the possibility of explaining the deviation from the standard expectation of the anomalous magnetic moment of the muon and the $W$-boson mass recently observed at Fermilab. We also summarize the astrophysical constraints from direct and indirect detection dark matter experiments. We finally conduct a thorough analysis of the cosmic phase transitions and the gravitational wave spectrum that are implied by the model and identify the parameter space in which the electroweak vacuum is reached after single and multiple phase transitions. We then discuss the prospects for observing the signal of such gravitational waves in near future experiments such as LISA, BBO or DECIGO.