Higgs Dynamics during Inflation
  We investigate inflationary Higgs dynamics and constraints on the Standard
Model parameters assuming the Higgs potential, computed to next-to-next leading
order precision, is not significantly affected by new physics. For a high
inflationary scale $H\sim 10^{14}$ GeV suggested by BICEP2, we show that the
Higgs is a light field subject to fluctuations which affect its dynamics in a
stochastic way. Starting from its inflationary value the Higgs must be able to
relax to the Standard Model vacuum well before the electroweak scale. We find
that this is consistent with the high inflationary scale only if the top mass
$m_t$ is significantly below the best fit value. The region within $2\sigma$
errors of the measured $m_t$, the Higgs mass $m_h$ and the strong coupling
$\alpha_s$ and consistent with inflation covers approximately the interval $m_t
\lesssim 171.8\,{\rm GeV} + 0.538(m_h-125.5\,{\rm GeV})$ with $125.4\,{\rm
GeV}\lesssim m_h\lesssim 126.3\,{\rm GeV}$. If the low top mass region could be
definitively ruled out, the observed high inflationary scale alone, if
confirmed, would seem to imply new physics necessarily modifying the Standard
Model Higgs potential below the inflationary scale.
