Probing Planck-Scale Physics with High-Frequency Gravitational Waves

TL;DR

This paper proposes a novel method to test quantum gravity theories by analyzing the gravitational-wave background from evaporating primordial black holes, focusing on spectral features that reveal Planck-scale physics.

Contribution

It introduces a framework linking quantum gravity models to gravitational wave spectra via black hole temperature-mass relations, enabling observational tests of quantum gravity.

Findings

Spectral peak shifts up to ten decades in frequency for different models.

Distinct peak morphologies can discriminate between quantum gravity scenarios.

Spectral shape differences are independent of cosmological parameters.

Abstract

We develop a framework for testing quantum gravity through the stochastic gravitational-wave background produced by evaporating near-Planck-mass primordial black holes. Because gravitons free-stream from the emission region without rescattering, they preserve a direct spectral record of the black-hole temperature--mass relation $T(M)$, a relation that is erased for all other Hawking-radiated species by rapid thermalization. We translate six representative phenomenological beyond-semiclassical frameworks (the generalized uncertainty principle, loop quantum gravity, noncommutative geometry, asymptotic safety, string/Hagedorn physics, and tunneling backreaction) into distinct $T(M)$ parametrizations and compute the resulting gravitational wave spectra numerically. Modifications that suppress $T(M)$ shift the spectral peak by up to ten decades in frequency, in some cases into the sensitivity bands of next-generation interferometers or resonant-cavity detectors, while models imposing a hard evaporation cutoff produce distinctive peak morphologies that discriminate between quantum-gravity scenarios. We further discuss the impact of different choices for post-inflationary conditions in the very early universe. We find that the relative spectral displacement between the standard Hawking prediction and any modified model is cosmology-independent, hence spectral shape rather than absolute peak frequency provides the cleanest probe of Planck-scale physics.