  During inflation, scalar fields with masses less than the Hubble scale
acquire vacuum expectation values (vevs) via stochastic processes driven by
quantum fluctuations. For nearly massless spectator scalars transforming
nontrivially under a continuous symmetry group, we demonstrate that the
evolution of the vev depends on the dimensionality of the scalar field space.
Fields in larger representations both attain larger vacuum expectation values
and converge more rapidly to equilibrium. We present an argument demonstrating
how this higher-dimensional evolution can be obtained in unitary gauge for
fields transforming under local symmetries with a mass gap that is small
compared to the Hubble scale. Finally, we show that accounting for the full
number of degrees of freedom in the Standard Model Higgs multiplet tightens
Higgs stability constraints on the inflationary scale at the percent level and
has more dramatic consequences for both the vev and the energy stored in the
Higgs field after inflation.
