Vacuum Stability in the Early Universe and the Backreaction of Classical
  Gravity
  In the case of a metastable electroweak vacuum the quantum corrected
effective potential plays a crucial role in the potential instability of the
Standard Model. In the Early Universe, in particular during inflation and
reheating, this instability can be triggered leading to catastrophic vacuum
decay. We discuss how the large spacetime curvature of the Early Universe can
be incorporated in the calculation and in many cases significantly modify the
flat space prediction. The two key new elements are the unavoidable generation
of the non-minimal coupling between the Higgs field and the scalar curvature of
gravity and a curvature induced contribution to the running of the constants.
For the minimal set up of the Standard Model and a decoupled inflation sector
we show how a metastable vacuum can lead to very tight bounds for the
non-minimal coupling. We also discuss a novel and very much related dark matter
generation mechanism.
