Constraints on Lorentz invariance violation from gamma-ray burst GRB090510

We obtain modified dispersion relations by requiring the vanishing of determinant of inverse of modified photon propagators in Lorentz invariance violation (LIV) theory. Inspired by these dispersion relations, we give a more general dispersion relation with less assumption and apply it to the recent observed gamma-ray burst GRB090510 to extract various constraints on LIV parameters. We find that the constraint on quantum gravity mass is slightly larger than the Planck mass but is consistent with the other recent observations, so the corresponding LIV coefficient $\xi_1$ has reached the natural order ($o(1)$) as one expects. From our analysis, the linear LIV corrections to photon group velocity might be not excluded yet.

💡 Research Summary

This paper presents a comprehensive study investigating Lorentz Invariance Violation (LIV) by deriving modified photon dispersion relations from theoretical frameworks and applying them to observational data from the gamma-ray burst GRB090510.

The theoretical core of the work involves systematically deriving modified dispersion relations for photons within various LIV frameworks. The authors employ a unified methodological approach: requiring the determinant of the inverse of the modified photon propagator to vanish. This technique is applied to three specific models: 1) the Standard Model Extension (SME) with background tensor fields, 2) an effective field theory incorporating non-renormalizable dimension-5 operators (Myers-Pospelov model), and 3) a bosonic field theory inspired by Hořava’s anisotropic scaling gravity. From these models, specific energy-dependent dispersion relations are obtained, each indicating a potential deviation from the conventional E²=p² relation at high energies.

Inspired by these model-specific results, the authors propose a more general, phenomenological dispersion relation: E² = p²