We update the phenomenology of gauge singlet extensions of the Standard Model scalar sector and their implications for the electroweak phase transition. Considering the introduction of one real scalar singlet to the scalar potential, we analyze present constraints on the potential parameters from Higgs coupling measurements at the Large Hadron Collider (LHC) and electroweak precision observables for the kinematic regime in which no new scalar decay modes arise. We then show how future precision measurements of Higgs boson signal strengths and Higgs self-coupling could probe the scalar potential parameter space associated with a strong first-order electroweak phase transition. We illustrate using benchmark precision for several future collider options, including the High Luminosity LHC (HL-LHC), the International Linear Collider (ILC), TLEP, China Electron Positron Collider (CEPC), and a 100 TeV proton-proton collider, such as the Very High Energy LHC (VHE-LHC) or the Super proton-proton Collider (SPPC). For the regions of parameter space leading to a strong first order electroweak phase transition, we find that there exists considerable potential for observable deviations from purely Standard Model Higgs properties at these prospective future colliders.
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