Propagation in a thermal graviton background

TL;DR

This paper investigates how a thermal graviton background affects scalar particle propagation, revealing Lorentz invariance breaking at finite momentum but not at high momentum, and showing the decay rate to equilibrium vanishes at one loop.

Contribution

It provides the first calculation of one-loop radiative corrections to scalar propagators in a thermal graviton background, highlighting Lorentz invariance breaking and its momentum dependence.

Findings

Lorentz invariance breaking terms vanish at high momentum

Imaginary part of self-energy vanishes at one loop

Thermal corrections influence scalar propagation in gravity backgrounds

Abstract

It is well known that radiative corrections evaluated in nontrivial backgrounds lead to effective dispersion relations which are not Lorentz invariant. Since gravitational interactions increase with energy, gravity-induced radiative corrections could be relevant for the trans-Planckian problem. As a first step to explore this possibility, we compute the one-loop radiative corrections to the self-energy of a scalar particle propagating in a thermal bath of gravitons in Minkowski spacetime. We obtain terms which originate from the thermal bath and which indeed break the Lorentz invariance that possessed the propagator in the vacuum. Rather unexpectedly, however, the terms which break Lorentz invariance vanish in the high three-momentum limit. We also found that the imaginary part, which gives the rate of approach to thermal equilibrium, vanishes at one loop.