Quintessential Inflation for Exponential Type Potentials: Scaling and Tracker Behavior

TL;DR

This paper investigates exponential potentials in quintessential inflation, showing that initial conditions during slow roll do not lead to scaling solutions, implying no late-time mechanism is needed for cosmic acceleration.

Contribution

It demonstrates that for exponential potentials, slow roll initial conditions do not result in scaling solutions, challenging previous assumptions about late-time behavior in quintessential inflation.

Findings

Slow roll conditions do not belong to the basin of attraction of scaling solutions.

No late-time mechanism is necessary for cosmic acceleration in this model.

Scaling solutions are not naturally reached from typical initial conditions.

Abstract

We will show that for exponential type potentials, which are used to depict quintessential inflation, the solutions whose initial conditions take place during the slow roll phase in order to describe correctly the inflationary period do not belong to the basin of attraction of the scaling solution -a solution of the scalar field equation whose energy density scale as the one of the fluid component of the universe during radiation or the matter domination period-, meaning that a late time mechanism to exit this behavior and depict correctly the current cosmic acceleration is not needed.