Probing the Electroweak Phase Transition with Higgs Factories and
  Gravitational Waves
  After the discovery of the Higgs boson, understanding the nature of
electroweak symmetry breaking and the associated electroweak phase transition
has become the most pressing question in particle physics. Answering this
question is a priority for experimental studies. Data from the LHC and future
lepton collider-based Higgs factories may uncover new physics coupled to the
Higgs boson, which can induce the electroweak phase transition to become first
order. Such a phase transition generates a stochastic background of
gravitational waves, which could potentially be detected by a space-based
gravitational wave interferometer. In this paper, we survey a few classes of
models in which the electroweak phase transition is strongly first order. We
identify the observables that would provide evidence of these models at the LHC
and next-generation lepton colliders, and we assess whether the corresponding
gravitational wave signal could be detected by eLISA. We find that most of the
models with first order electroweak phase transition can be covered by the
precise measurements of Higgs couplings at the proposed Higgs factories. We
also map out the model space that can be probed with gravitational wave
detection by eLISA.
