  In this paper we study the possibility of probing for the absolute neutrino
mass and its variation with short Gamma Ray Burst (GRB). We have calculated the
flight time difference between a massive neutrino and a photon in two different
approaches to mass varying neutrinos. Firstly we parametrize the neutrino mass
as a function of redshift in a model independent way, then we consider two
specific models where the neutrino mass varies during the evolution of the
Quintessence fields. Our calculations show in general the value of the time
delay is changed substantially relative to a constant neutrino mass.
Furthermore our numerical results show that the flight time delay in these
models is expected to be larger than the duration time of the short GRB, which
opens a possibility of testing the scenario of mass varying neutrino with the
short GRB.
