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Lorentz Invariance Violation (LIV) manifesting itself by energy dependentmodification of standard relativistic dispersion relation has recentlyattracted a considerable attention. Ellis et al. previously investigated theenergy dependent time offsets in different energy bands on a sample of gammaray bursts and, assuming standard cosmological model, they found a weakindication for redshift dependence of time delays suggestive of LIV. Goingbeyond the $\Lambda$CDM cosmology we extend this analysis considering also fouralternative models of dark energy (quintessence with constant and variableequation of state, Chaplygin gas and brane-world cosmology). It turns out thatthe effect noticed by Ellis et al. is also present in those models and is thestrongest for quintessence with variable equation of state.

Lorentz Invariance Violation induced time delays in GRBs in different cosmological models