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  • Open Access

Bounds on the covariant diffusion and drift parameters from the stochastic GW background using LISA

Giorgio Mentasti* and Arad Nasiri†

  • *Contact author: giorgio@apc.in2p3.fr
  • †Contact author: a.nasiri21@imperial.ac.uk
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Phys. Rev. D 113, 084043 – Published 17 April, 2026

DOI: https://doi.org/10.1103/wkyz-8yy5

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, κ1 and κ2, 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 with the Laser Interferometer Space Antenna can constrain the parameters down to a value of κ1,κ2≲10−56  kg m2 s−3.

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Phys. Rev. D 113, 084043– Published 17 April, 2026
  • Received 24 July 2025
  • Accepted 12 March 2026
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