  The mass-varying neutrino scenario is analyzed for three trial quintessence
potentials (Ferreira-Joyce, inverse exponential, and thawing oscillating). The
neutrino mass is generated via Yukawa coupling to the scalar field which
represents dark energy. The inverse exponential and oscillating potentials are
shown to successfully generate the neutrino masses in the range $m \sim
10^{-2}-10^{-3}~$eV and to yield the current dark energy density in the regime
of the late-time acceleration of the Universe. Depending on the choice of
potentials, the acceleration could occur in two different regimes: (1) the
regime of instability, and (2) the stable regime. The first regime of
instability is after the Universe underwent a first-order transition and is
rolling toward the new stable vacuum. The imaginary sound velocity $c^2_s < 0$
in this regime implies growing fluctuations of the neutrino density
(clustering). In the second regime, the Universe smoothly changes its stable
states via a continuous transition. Since $c^2_s > 0$, the neutrino density is
stable. For all cases the predicted late-time acceleration of the Universe is
asymptotically very close to that of the $\Lambda$CDM model. Further extensions
of the theory to modify the neutrino sector of the Standard Model and to
incorporate inflation are also discussed. It is also shown that in the stable
regimes where the neutrino mass is given by the minimum of the thermodynamic
potential, the tree-level dynamics of the scalar field is robust with respect
to one-loop bosonic and fermionic corrections to the potential.
