A Cosmological Signature of the SM Higgs Instability: Gravitational
  Waves
  A fundamental property of the Standard Model is that the Higgs potential
becomes unstable at large values of the Higgs field. For the current central
values of the Higgs and top masses, the instability scale is about $10^{11}$
GeV and therefore not accessible by colliders. We show that a possible
signature of the Standard Model Higgs instability is the production of
gravitational waves sourced by Higgs fluctuations generated during inflation.
We fully characterise the two-point correlator of such gravitational waves by
computing its amplitude, the frequency at peak, the spectral index, as well as
their three-point correlators for various polarisations. We show that,
depending on the Higgs and top masses, either LISA or the Einstein Telescope
and Advanced-Ligo, could detect such stochastic background of gravitational
waves. In this sense, collider and gravitational wave physics can provide
fundamental and complementary informations. Furthermore, the consistency
relation among the three- and the two-point correlators could provide an
efficient tool to ascribe the detected gravitational waves to the Standard
Model itself. Since the mechanism described in this paper might also be
responsible for the generation of dark matter under the form of primordial
black holes, this latter hypothesis may find its confirmation through the
detection of gravitational waves.
