Quintessential inflation from Lorentzian slow roll

From the assumption that the slow-roll parameter $$\varepsilon $$ has a Lorentzian form as a function of the e-fold number N, a successful model of a quintessential inflation is obtained, as succinctly studied in [1]. The form corresponds to the vacuum energy both in the inflationary and in the dark-energy epochs and satisfies the condition to climb from small values of $$\varepsilon $$ to 1 at the end of the inflationary epoch. We find the corresponding scalar quintessential inflationary potential with two flat regions. Moreover, a reheating mechanism is suggested with numerical estimation for the homogeneous evolution of the universe. The suggested mechanism is consistent with the BBN bound