Unrestored Electroweak Symmetry
  The commonly assumed cosmological history of our universe is that at
early-times and high-temperatures the universe went through an ElectroWeak
Phase Transition (EWPT). Assuming an EWPT, and depending on its strength, there
are many implications for baryogenesis, gravitational waves, and the evolution
of the universe in general. However, it is not true that all spontaneously
broken symmetries at zero-temperature are restored at high-temperature. In
particular the idea of "inverse symmetry breaking" has long been established in
scalar theories with evidence from both perturbative and lattice calculations.
In this letter we demonstrate that with a simple extension of the SM it is
possible that the ElectroWeak (EW) symmetry was always broken or only
temporarily passed through a symmetry restored phase. These novel phase
histories have many cosmological and collider implications that we discuss. The
model presented here serves as a useful benchmark comparison for future
attempts to discern the phase of our universe at $T\gtrsim$ a few GeV.
