Hierarchical Test of Lorentz Invariance with Gamma-Ray Burst Spectral-Lag Measurements

TL;DR

This study uses a hierarchical Bayesian approach to analyze 32 gamma-ray bursts, providing robust constraints on Lorentz invariance violation energy scales and finding no significant evidence for LIV signatures.

Contribution

It introduces a hierarchical Bayesian method to combine GRB spectral lag data, accounting for systematics, to set robust limits on LIV energy scales.

Findings

Lower limit on linear LIV energy scale: 4.37 x 10^{16} GeV

Lower limit on quadratic LIV energy scale: 3.02 x 10^{8} GeV

Approximately 90 ext{% probability that LIV energy scale is below Planck scale

Abstract

Gamma-ray bursts (GRBs) are among the most potent probes of Lorentz invariance violation (LIV), offering direct constraints on the quantum gravity energy scale ($E_{\rm QG}$) based on observations of energy-dependent time lags. Individual GRBs with well-defined positive-to-negative lag transitions have been used to set lower limits on $E_{\rm QG}$, but they suffer from uncertainties of spectral-lag measurements and systematics due to theoretical modeling of each burst. Here, we combine observations of 32 GRBs with positive-to-negative lag transitions to derive a statistically robust constraint on $E_{\rm QG}$ through hierarchical Bayesian inference. We find that the dominant systematic uncertainty in LIV constraints arises from the intrinsic lag modeling. Accounting for this uncertainty with cubic spline interpolation, we derive robust limits of $E_{\rm QG,1} \ge 4.37 \times 10^{16}$~GeV for linear LIV and $E_{\rm QG,2} \ge 3.02 \times 10^{8}$~GeV for quadratic LIV. We find that the probability for LIV, i.e., $E_{\rm QG,1}$ being below the Planck scale, is estimated to be around 90\%, which we conclude as no significant evidence for LIV signatures in current GRB spectral lag observations. Our hierarchical approach provides a rigorous statistical framework for future LIV searches and can be extended to incorporate multi-messenger observations.