  Determining the thermal history of electroweak symmetry breaking (EWSB) is an
important challenge for particle physics and cosmology. Lattice simulations
indicate that EWSB in the Standard Model (SM) occurs through a crossover
transition, while the presence of new physics beyond the SM could alter this
thermal history. The occurrence of a first order EWSB transition would be
particularly interesting, providing the needed pre-conditions for generation of
the cosmic matter-antimatter asymmetry and sources for potentially observable
gravitational radiation. I provide simple, generic arguments that if such an
alternate thermal history exists, the new particles involved cannot be too
heavy with respect to the SM electroweak temperature, nor can they interact too
feebly with the SM Higgs boson. These arguments do not rely on the decoupling
limit. I derive corresponding quantitative expectations for masses and
interaction strengths which imply that their effects could in principle be
observed (or ruled out) by prospective next generation high energy colliders.
The simple, generic arguments provide a quantitative, parametric understanding
of results obtained in a wide range of explicit model studies; relate them
explicitly to the electroweak temperature; and delineate broad contours of
collider phenomenology pertaining to a non-standard history of EWSB.
