  An essential goal of the Higgs physics program at the LHC and beyond is to
explore the nature of the Higgs potential and shed light on the mechanism of
electroweak symmetry breaking. An important class of models defining the
strength and order of the electroweak phase transition is driven by the Higgs
boson coupling to a light new state. This Snowmass white paper points out the
existence of a region of parameter space where a strongly first order
electroweak phase transition is compatible with exotic decays of the SM-like
Higgs boson. A dedicated search for exotic Higgs decays can actively explore
this framework at the Large Hadron Collider (LHC), while future exotic Higgs
decay searches at the high-luminosity LHC and future Higgs factories will be
vital to conclusively probe the scenario.
