# Scaling solutions in quintessential inflation

## TL;DR

This paper investigates how quintessential inflation models can naturally produce scaling solutions during early cosmic epochs and transition to late-time acceleration, emphasizing the role of initial conditions and potential shapes.

## Contribution

It demonstrates that a single exponential tail in the potential can account for the universe's evolution without requiring initial conditions in the scaling solution's basin.

## Key findings

- Scaling solutions are relevant during radiation and matter epochs.
- A single exponential tail in the potential suffices for cosmic evolution.
- Quintessential inflation models can naturally transition from scaling to acceleration.

## Abstract

In quintessence scalar field theories, the presence of scaling solutions are important during the radiation and matter epoch due to having their attractor character. Usually, it is assumed that the initial conditions of the quintessence field are in the basin of attraction of the scaling solutions. However, in order to reproduce the current cosmic acceleration, at late times, a mechanism to exit this behavior is needed. In the present work we show that the quintessential inflation models could be an excellent candidate to exhibit the above behavior. However, the crucial point of quintessential inflation is that the initial conditions has to be taken during the inflation, and at the beginning of the radiation era, the scalar field does not belong to the basin of attraction of the scaling solution. This means that, in the case where quintessence is depicted via exponential potentials, only a single exponential in the tail of the { quintessential inflation} potential is enough to depict the evolution of our universe.