Current discussions of the allowed two-Higgs-doublet model (2HDM) parameter space after LHC Run 1 and the prospects for Run 2 are commonly phrased in the context of a quasi-degenerate spectrum for the new scalars. Here we discuss the generic situation of a 2HDM with a non-degenerate spectrum for the new scalars. This is highly motivated from a cosmological perspective since it naturally leads to a strongly first order electroweak phase transition that could explain the matter-antimatter asymmetry in the Universe. While constraints from measurements of Higgs signal strengths do not change, those from searches of new scalar states get modified dramatically once a non-degenerate spectrum is considered.
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