Lorentz Invariance Violation (LIV) manifesting itself by energy dependent
modification of standard relativistic dispersion relation has recently
attracted a considerable attention. Ellis et al. previously investigated the
energy dependent time offsets in different energy bands on a sample of gamma
ray bursts and, assuming standard cosmological model, they found a weak
indication for redshift dependence of time delays suggestive of LIV. Going
beyond the ΛCDM cosmology we extend this analysis considering also four
alternative models of dark energy (quintessence with constant and variable
equation of state, Chaplygin gas and brane-world cosmology). It turns out that
the effect noticed by Ellis et al. is also present in those models and is the
strongest for quintessence with variable equation of state.Comment: 14 pages, 1 figur