# Emergence of cosmological scaling behavior in asymptotic regime

## TL;DR

This paper analyzes a scalar field with specific potentials, demonstrating that a cosmological scaling solution emerges as an attractor in the asymptotic regime, with implications for quintessential inflation models.

## Contribution

It introduces a class of potentials where the scaling solution acts as an attractor, expanding understanding of scalar field dynamics in cosmology.

## Key findings

- Scaling solution is an attractor in the asymptotic regime.
- Identified fixed points in the dynamical system.
- Potential application to quintessential inflation models.

## Abstract

In this paper we consider a scalar field system with a class of potentials given by the expression, $V(\phi)\propto \phi^m {\rm exp}({-\lambda \phi^n/{M^n_{Pl}}})$; $m\geqslant 0, n>1$ for which $\Gamma=V_{\phi \phi}V/V^2_{\phi}\to 1 $ as $|\phi|\to \infty$. We carry out dynamical analysis for the underlying system choosing a suitable set of autonomous variables and find all the fixed points. In particular, we show that the scaling solution is an attractor of the system in the asymptotic regime. We indicate the application of the solution to models of quintessential inflation.