# Constraints on quantum gravity and the photon mass from gamma ray bursts

Published in *Phys. Rev. D, 104(10):10351*, 2021

Recommended citation: D.J. Bartlett, H. Desmond, P.G. Ferreira and J. Jasche (2021). "Constraints on quantum gravity and the photon mass from gamma ray bursts." *Phys. Rev. D, 104(10):10351*.

## Abstract

Lorentz invariance violation in quantum gravity (QG) models or a nonzero photon mass, $m_\gamma$, would lead to an energy-dependent propagation speed for photons, such that photons of different energies from a distant source would arrive at different times, even if they were emitted simultaneously. By developing source-by-source, Monte Carlo-based forward models for such time delays from gamma ray bursts, and marginalising over empirical noise models describing other contributions to the time delay, we derive constraints on $m_\gamma$ and the QG length scale, $\ell_{\rm QG}$, using spectral lag data from the BATSE satellite. We find $m_\gamma < 4.0 \times 10^{-5} \, h \, {\rm eV}/c^2$ and $\ell_{\rm QG} < 5.3 \times 10^{-18} \, h \, {\rm \, GeV^{-1}}$ at 95\% confidence, and demonstrate that these constraints are robust to the choice of noise model. The QG constraint is among the tightest from studies which consider multiple gamma ray bursts and the constraint on $m_\gamma$, although weaker than from using radio data, provides an independent constraint which is less sensitive to the effects of dispersion by electrons.

*Lower limits on the quantum gravity energy scale (\(1 / \ell_{\rm QG}\)) from time delay studies which use multiple astrophysical sources. Our work provides the tightest constraint to date. The dashed vertical line is the Planck energy, and it is expected that the quantum gravity energy scale has approximately this value.*