Constraints on the quantum gravity scale from kappa - Minkowski spacetime

TL;DR

This paper develops a comprehensive framework for analyzing modified dispersion relations in kappa-Minkowski spacetime, deriving bounds on quantum gravity scale from gamma-ray burst data, and clarifying the role of different realizations.

Contribution

It introduces a general framework for modified dispersion relations in kappa-Minkowski spacetime, covering all known cases and enabling bounds on quantum gravity scale from observational data.

Findings

Some realizations provide bounds on quadratic corrections to the quantum gravity scale.

The quantum gravity scale could still be the Planck scale within the framework.

Coefficients in dispersion relations can be fitted using gamma-ray burst data.

Abstract

We compare two versions of deformed dispersion relations (energy vs momenta and momenta vs energy) and the corresponding time delay up to the second order accuracy in the quantum gravity scale (deformation parameter). A general framework describing modified dispersion relations and time delay with respect to different noncommutative kappa -Minkowski spacetime realizations is firstly proposed here and it covers all the cases introduced in the literature. It is shown that some of the realizations provide certain bounds on quadratic corrections, i.e. on quantum gravity scale, but it is not excluded in our framework that quantum gravity scale is the Planck scale. We also show how the coefficients in the dispersion relations can be obtained through a multiparameter fit of the gamma ray burst (GRB) data.