Quintessential Inflation from Lorentzian Slow Roll

TL;DR

This paper proposes a new model of quintessential inflation based on a Lorentzian form of the slow roll parameter, resulting in a potential with two flat regions and a reheating mechanism compatible with BBN constraints.

Contribution

It introduces a novel Lorentzian slow roll parameter form leading to a scalar potential with two flat regions for quintessential inflation.

Findings

Derived a scalar potential with two flat regions for inflation and dark energy.

Proposed a reheating mechanism consistent with BBN bounds.

Numerically estimated the universe's homogeneous evolution during reheating.

Abstract

From the assumption that the slow roll parameter $\epsilon$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained, as succinctly studied in \cite{Benisty:2020xqm}. 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 $\epsilon$ 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.