  Future measurements of primordial non-Gaussianity can reveal cosmologically
produced particles with masses of order the inflationary Hubble scale and their
interactions with the inflaton, giving us crucial insights into the structure
of fundamental physics at extremely high energies. We study gauge-Higgs
theories that may be accessible in this regime, carefully imposing the
constraints of gauge symmetry and its (partial) Higgsing. We distinguish two
types of Higgs mechanisms: (i) a standard one in which the Higgs scale is
constant before and after inflation, where the particles observable in
non-Gaussianities are far heavier than can be accessed by laboratory
experiments, perhaps associated with gauge unification, and (ii) a
"heavy-lifting" mechanism in which couplings to curvature can result in Higgs
scales of order the Hubble scale during inflation while reducing to far lower
scales in the current era, where they may now be accessible to collider and
other laboratory experiments. In the heavy-lifting option,
renormalization-group running of terrestrial measurements yield predictions for
cosmological non-Gaussianities. If the heavy-lifted gauge theory suffers a
hierarchy problem, such as does the Standard Model, confirming such predictions
would demonstrate a striking violation of the Naturalness Principle. While
observing gauge-Higgs sectors in non-Gaussianities will be challenging given
the constraints of cosmic variance, we show that it may be possible with
reasonable precision given favorable couplings to the inflationary dynamics.
