Effective 2HDM Yukawa Interactions and a Strong First-Order Electroweak Phase Transition

The top quark as the heaviest particle in the Standard Model (SM) defines an important mass scale for Higgs physics and the electroweak scale itself. It is therefore a well-motivated degree of freedom which could reveal the presence of new interactions beyond the SM. Correlating modifications of the top-Higgs interactions in the 2-Higgs-Doublet Model (2HDM), we analyse effective field theory deformations of these interactions from the point of view of a strong first-order electroweak phase transition (SFOEWPT). We show that such modifications are compatible with current Higgs data and that an SFOEWPT can be tantamount to a current overestimate of exotic Higgs searches' sensitivity at the LHC in $t\bar t$ and four top quark final states. We argue that these searches remain robust from the point of accidental signal-background interference so that the current experimental strategy might well lead to 2HDM-like discoveries in the near future.