  Recently a new kind of quintessential inflation coming from the Lorentzian
distribution has been introduced in [1,2]. The model leads to a very simple
potential, which basically depends on two parameters, belonging to the class of
$\alpha$-attractors and depicting correctly the early and late time
accelerations of our universe. The potential emphasizes a {\it cosmological
see-saw mechanism} (CSSM) that produces a large inflationary vacuum energy in
one side of the potential and a very small value of dark energy on the right
hand side of the potential. {Here we show that the model agrees with the recent
observations and with the reheating constraints. Therefore the model gives a
reasonable scenario beyond the standard $\Lambda$CDM that includes the
inflationary epoch.}
