  In this paper we consider the possibility of neutrino mass varying during the
evolution of the Universe and study its implications on leptogenesis.
Specifically, we take the minimal seesaw model of neutrino masses and introduce
a coupling between the right-handed neutrinos and the dark energy scalar field,
the Quintessence. In our model, the right-handed neutrino masses change as the
Quintessence scalar evolves. We then examine in detail the parameter space of
this model allowed by the observed baryon number asymmetry. Our results show
that it is possible to lower the reheating temperature in this scenario in
comparison with the case that the neutrino masses are unchanged, which helps
solve the gravitino problem. Furthermore, a degenerate neutrino mass patten
with $m_i$ larger than the upper limit given in the minimal leptogenesis
scenario is permitted.
