Gauge hierarchy from electroweak vacuum metastability
  We consider the possibility that the gauge hierarchy is a byproduct of the
metastability of the electroweak vacuum, i.e., that whatever mechanism is
responsible for the latter also sets the running Higgs mass to a value smaller
than its natural value by many orders of magnitude. This perspective is
motivated by the early-time framework for eternal inflation put forth recently,
which favors vacua that are relatively short-lived, but applies more generally
to any theoretical approach predicting that our vacuum should be metastable. We
find that the metastability of the electroweak vacuum, together with the
requirement that such a non-trivial vacuum exists, requires the Higgs mass to
be smaller than the instability scale by around one order of magnitude. While
this bound is quite weak in the Standard Model (SM), as the instability scale
is $\sim 10^{11}$ GeV, simple and well-motivated extensions of the SM -
concretely, the $\nu$MSM with an approximate $B-\tilde{L}$ symmetry and the
minimal SU(4)/Sp(4) composite Higgs model - can significantly tighten the bound
by lowering the instability scale. We find that the bound can be brought down
to $\simeq 10$ TeV where our perturbative treatment of the decay rate becomes
unreliable. Our results imply that, assuming the SM symmetry breaking pattern,
small running Higgs masses are a universal property of theories giving rise to
metastability, suggesting a common origin of the two underlying fine-tunings
and providing a strong constraint on any attempt to explain metastability.
