Mass Varying Neutrinos, Quintessence, and the Accelerating Expansion of
  the Universe
  We analyze the Mass Varying Neutrino (MaVaN) scenario. We consider a minimal
model of massless Dirac fermions coupled to a scalar field, mainly in the
framework of finite temperature quantum field theory. We demonstrate that the
mass equation we find has non-trivial solutions only for special classes of
potentials, and only within certain temperature intervals. We give most of our
results for the Ratra-Peebles Dark Energy (DE) potential. The thermal
(temporal) evolution of the model is analyzed. Following the time arrow, the
stable, metastable and unstable phases are predicted. The model predicts that
the present Universe is below its critical temperature and accelerates. At the
critical point the Universe undergoes a first-order phase transition from the
(meta)stable oscillatory regime to the unstable rolling regime of the DE field.
This conclusion agrees with the original idea of quintessence as a force making
the Universe roll towards its true vacuum with zero \Lambda-term. The present
MaVaN scenario is free from the coincidence problem, since both the DE density
and the neutrino mass are determined by the scale M of the potential. Choosing
M ~ 10^{-3} eV to match the present DE density, we can obtain the present
neutrino mass in the range m ~ 10^{-2}-1 eV and consistent estimates for other
parameters of the Universe.
