Quintessential Inflation from Lorentzian Slow Roll

From the assumption that the slow roll parameter ε has a Lorentzian form as a function of the e-folds number N, 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 and satisfies the condition to climb from small values of ε 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.