Lorentzian quintessential inflation
From the assumption that the slow-roll parameter [Formula: see text] has a Lorentzian form as a function of the e-folds number [Formula: see text], a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of [Formula: see text] to [Formula: see text] at the end of the inflationary epoch. At the late universe, [Formula: see text] becomes small again and this leads to the dark energy epoch. The observables that the models predict fits with the latest Planck data: [Formula: see text]. Naturally, a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appearance, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions — one inflationary and one as a dark energy with slow-roll behavior.