Inflaton-driven early dark energy
  By arranging the control parameters, we examine whether the mass varying
neutrino model PRD 103, 063540 (2021), enabling one to unify inflation with the
present dark energy, can be used for producing an early dark energy. The model
works in the following way. At early stages of the Big-Bang, the inflaton
trapped in the minimum at $\phi = 0$ gets uplifted due to interaction with
neutrinos and starts to roll down to one of the degenerate minima of the
effective potential and after a while gets anchored at this minimum, which in
turn evolves in time very slowly. Correspondingly, the early dark energy taking
place as a result of this dynamical symmetry breaking also varies in time very
slowly. Shortly before the recombination epoch, however, the symmetry is
restored and early dark energy disappears. A typical problem of the mass
varying neutrino models is that they can hardly provide the needed amount of
early dark energy at the tree-level because of smallness of neutrino masses.
Nevertheless, the quantum fluctuations of $\phi$ can do the job in providing
sufficient early dark energy under assumption that inflationary energy scale is
of the order of $1$\,TeV. Radiative as well as thermal corrections coming from
the neutrino sector do not affect the model significantly. As for the gravity
induced corrections to the effective potential - they can be safely ignored.
