Gauge-Independent Scales Related to the Standard Model Vacuum
  Instability
  The measured (central) values of the Higgs and top quark masses indicate that
the Standard Model (SM) effective potential develops an instability at high
field values. The scale of this instability, determined as the Higgs field
value at which the potential drops below the electroweak minimum, is about
$10^{11}$ GeV. However, such a scale is unphysical as it is not gauge-invariant
and suffers from a gauge-fixing uncertainty of up to two orders of magnitude.
Subjecting our system, the SM, to several probes of the instability (adding
higher order operators to the potential; letting the vacuum decay through
critical bubbles; heating up the system to very high temperature; inflating it)
and asking in each case physical questions, we are able to provide several
gauge-invariant scales related with the Higgs potential instability.
