Cosmological bounds on TeV-scale physics and beyond
  We study the influence of the fluctuations of a Lorentz invariant and
conserved vacuum on cosmological metric perturbations, and show that they
generically blow up in the IR. We compute this effect using the
K\"all\'en-Lehmann spectral representation of stress correlators in generic
quantum field theories, as well as the holographic bound on their entanglement
entropy, both leading to an IR cut-off that scales as the fifth power of the
highest UV scale (in Planck units). One may view this as analogous to the
Heisenberg uncertainty principle, which is imposed on the phase space of
gravitational theories by the Einstein constraint equations. The leading effect
on cosmological observables come from anisotropic vacuum stresses which imply:
i) any extension of the standard model of particle physics can only have masses
(or resonances) $\lesssim$ 24 TeV, and ii) perturbative quantum field theory or
quantum gravity becomes strongly coupled beyond a cut-off scale of
$\Lambda\lesssim1$ PeV. Such a low cut-off is independently motivated by the
Higgs hierarchy problem. This result, which we dub the cosmological
non-constant problem, can be viewed as an extension of the cosmological
constant (CC) problem, demonstrating the non-trivial UV-IR coupling and (yet
another) limitation of effective field theory in gravity. However, it is more
severe than the old CC problem, as vacuum fluctuations cannot be tuned to
cancel due to the positivity of spectral densities or entropy. We thus predict
that future advances in cosmological observations and collider technology will
sandwich from above and below, and eventually discover, new (non-perturbative)
physics beyond the Standard Model within the TeV-PeV energy range.
