Cosmological implications of EW vacuum instability: constraints on the
  Higgs-curvature coupling from inflation
  The current experimentally measured parameters of the Standard Model (SM)
suggest that our Universe lies in a metastable electroweak vacuum, where the
Higgs field is prone to vacuum decay to a lower state with catastrophic
consequences. Our measurements dictate that such an event has not taken place
yet, despite the many different mechanisms that could have triggered it in our
past light-cone. The focus of our work has been to calculate the probability of
the false vacuum to decay during the period of inflation and use it to
constrain the last unknown renormalisable SM parameter $\xi$, which couples the
Higgs field with space-time curvature. More specifically, we derived lower
$\xi$-bounds from vacuum stability in three inflationary models: quadratic and
quartic chaotic inflation, and Starobinsky-like power-law inflation. We also
took the time-dependence of the Hubble rate into account both in the geometry
of our past light-cone and in the Higgs effective potential, which is
approximated with three-loop renormalisation group improvement supplemented
with one-loop curvature corrections.
