  Modern ideas in quantum gravity predict the possibility of Lorenz Invariance
Violation (LIV) manifested e.g. by energy dependent modification of standard
relativistic dispersion relation. In a recent paper Jacob and Piran proposed
that time of flight delays in high energy neutrinos emitted by gamma ray bursts
(GRBs) located at cosmological distances can become a valuable tool for setting
limits on LIV theories. However, current advances in observational cosmology
suggest that our Universe is dominated by dark energy with relatively little
guidance on its nature thus leading to several cosmological scenarios
compatible with observations.
  In this paper we raise the issue of how important, in the context of testing
LIV theories, is our knowledge of background cosmological model. Specifically
we calculate expected time lags for high-energy (100 TeV) neutrinos in
different cosmological models. Out of many particular models of dark energy we
focus on five: $\Lambda$CDM, quintessence, quintessence with time varying
equation of state, brane-world and generalized Chaplygin gas model as
representative for various competing approaches. The result is that uncertainty
introduced by our ignorance concerning the right phenomenological model
describing dark energy dominated universe is considerable and may obscure
bounds derived from studying time delays from cosmological sources.
