On the potentials yielding cosmological scaling solutions

TL;DR

This paper analyzes flat FRW cosmological models with a perfect fluid and scalar field, showing that positive, monotonous, asymptotically exponential potentials lead to scaling solutions that act as global attractors.

Contribution

It provides a phase-plane analysis demonstrating that such potentials universally produce scaling solutions in these cosmological models.

Findings

Scaling solutions are global attractors for the system.

Asymptotically exponential potentials lead to stable scaling behavior.

The analysis applies to positive, monotonous potentials.

Abstract

In the present work we perform a phase-plane analysis of the complete dynamical system corresponding to a flat FRW cosmological models with a perfect fluid and a self-interacting scalar field and show that every positive and monotonous potential which is asymptotically exponential yields a scaling solution as a global attractor.