Covariant diffusion and drift of the stochastic GW background with LISA

TL;DR

This paper explores how stochastic effects in quantum gravity can influence the propagation of gravitational waves, proposing a model that preserves Lorentz invariance and can be constrained by LISA observations, vastly improving existing bounds.

Contribution

The study introduces a Lorentz-invariant stochastic model for massless particle diffusion affecting gravitational waves, with parameters constrained by CMB data and potentially measurable by LISA.

Findings

LISA can improve bounds on diffusion parameters by over 12 orders of magnitude.

Detection of GW backgrounds can constrain parameters to below 10^{-56} kg·m^2·s^{-3}.

The model preserves Lorentz invariance unlike other quantum gravity modifications.

Abstract

We study the covariant diffusion and drift of massless particles on the light cone within the context of quantum gravity phenomenology. Unlike modified dispersion relations that violate Lorentz invariance and grow with frequency, this model introduces a stochastic correction to the massless geodesic equation while preserving Lorentz invariance, and is dominant at lower frequencies due to the larger spacetime support of long-wavelength modes. The effect is phenomenologically described by just two diffusion and drift parameters, $\kappa_1$ and $\kappa_2$, whose values are already constrained by measurements of the CMB blackbody spectrum. We show that a direct measurement and characterization of a gravitational wave (GW) background frequency spectrum can improve bounds on these diffusion and drift parameters by over 12 orders of magnitude compared to those from the CMB. In particular, we find that detecting a GW background sourced by realistic models of first-order phase transitions or primordial black holes (PBH) with LISA can constrain the parameters down to a value of $\kappa_1,\,\kappa_2\lesssim 10^{-56}\,\text{kg}\,\text{m}^2\text{s}^{-3}$.