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We investigate the strength of the electroweak phase transition (EWPT) withinthe CP-violating 2-Higgs-Doublet Model (C2HDM). By applying a renormalisationscheme which allows efficient scans of the C2HDM parameter space, we analysethe possibility of a strong first order EWPT required for baryogenesis andstudy its phenomenological implications for the LHC. Like in the CP-conserving(real) 2HDM (R2HDM) we find that a strong EWPT favours mass gaps between thenon-SM-like Higgs bosons. These lead to prominent final states comprised ofgauge+Higgs bosons or pairs of Higgs bosons. In contrast to the R2HDM, theCP-mixing of the C2HDM also favours approximately mass degenerate spectra withdominant decays into SM particles. The requirement of a strong EWPT furtherallows us to distinguish the C2HDM from the R2HDM using the signal strengths ofthe SM-like Higgs boson. We additionally find that a strong EWPT requires anenhancement of the SM-like trilinear Higgs coupling at next-to-leading order(NLO) by up to a factor of 2.4 compared to the NLO SM coupling, establishinganother link between cosmology and collider phenomenology. We provide severalC2HDM benchmark scenarios compatible with a strong EWPT and all experimentaland theoretical constraints. We include the dominant branching ratios of thenon-SM-like Higgs bosons as well as the Higgs pair production cross section ofthe SM-like Higgs boson for every benchmark point. The pair production crosssections can be substantially enhanced compared to the SM and could beobservable at the high-luminosity LHC, allowing access to the trilinear Higgscouplings.

The CP-Violating 2HDM in Light of a Strong First Order Electroweak Phase Transition and Implications for Higgs Pair Production