Lifshitz scaling in CPT-even Lorentz-violating electrodynamics and GRB time delay

Abstract

In this work, we consider the Ho\v{r}ava-Lifshitz scaling to rewrite higher-order derivatives in Lorentz-violating CPT-even electrodynamics. The possibility of the Lorentz invariance violation being originally suppressed by the quantum gravity energy scale $M_{\rm QG}$, may be indeed circumvented in a scenario with anisotropy between space and time above certain intermediate energy scale $\Lambda_{\rm HL} \ll M_{\rm QG}$. To test the model, we have used observational results of a cosmological time delay between high and low energy photons from gamma ray bursts (GRB090510) event. For specific values of the Lifshitz critical exponent, we have found interesting lower bounds on the values of $M_{\rm QG}$.