  We review the well-known Peebles-Vilenkin (PV) quintessential inflation model
and discuss its possible improvements in agreement with the recent
observations. The improved PV model depends only on two parameters: the
inflaton mass $m$, and another smaller mass $M$; where the latter has to be
chosen in order to undertake that, at present time, the dark energy density of
the universe is approximately about 70\% of the total energy budget of the
universe. The value of the inflaton mass $m$ is calculated using the
observational value of the power spectrum of the scalar perturbations, and the
value of mass $M$, which depends on the reheating temperature, is calculated by
solving the corresponding dynamical system whose initial conditions are taken
at the matter-radiation equality and are obtained from three observational
data: the red shift at the matter-radiation equality, the ratio of the matter
energy density to the critical one at the present time and the current value of
the Hubble parameter.
