A curvature bound from gravitational catalysis in thermal backgrounds

TL;DR

This paper derives a thermal curvature bound to prevent gravitational catalysis, ensuring the existence of light fermions in the universe, and applies it to quantum gravity scenarios like asymptotic safety.

Contribution

It introduces a temperature-dependent curvature bound that constrains quantum gravity models to avoid inducing large fermion masses.

Findings

Finite temperature relaxes the curvature bound.

Curvature dependence is strongly influenced by details of spacetime.

The bound constrains the number of fermion flavors in quantum gravity.

Abstract

We investigate the phenomenon of gravitational catalysis, i.e., curvature-induced chiral symmetry breaking and fermion mass generation, at finite temperature. Using a scale-dependent analysis, we derive a thermal bound on the curvature of local patches of spacetime. This bound quantifies regions in parameter space that remain unaffected by gravitational catalysis and thus are compatible with the existence of light fermions as observed in Nature. While finite temperature generically relaxes the curvature bound, we observe a comparatively strong dependence of the phenomenon on the details of the curvature. Our bound can be applied to scenarios of quantum gravity, as any realistic candidate has to accommodate a sufficient number of light fermions. We argue that our bound therefore represents a test for quantum gravity scenarios: a suitably averaged spacetime in the (trans-)Planckian regime that satisfies our curvature bound does not induce correspondingly large Planckian fermion masses by gravitational catalysis. The temperature dependence derived in this work facilitates to follow the fate of gravitational catalysis during the thermal history of the (quantum) universe. In an application to the Asymptotic Safety scenario of quantum gravity, our bound translates into a temperature-dependent upper bound on the number of fermion flavors.