Cosmological bounds on TeV-scale physics and beyond

TL;DR

This paper explores how quantum vacuum fluctuations influence cosmological perturbations, leading to bounds on new physics scales and suggesting the inevitability of discovering new physics between TeV and PeV energies.

Contribution

It introduces the cosmological non-constant problem, linking IR effects of vacuum fluctuations to bounds on particle masses and quantum gravity cut-offs, extending the cosmological constant problem.

Findings

Vacuum fluctuations imply an IR cutoff scaling as the fifth power of the UV scale.

Standard model extensions are limited to masses below approximately 24 TeV.

Quantum gravity becomes strongly coupled beyond a scale of about 1 PeV.

Abstract

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.