Quintessence: Quadratic potentials

TL;DR

This paper develops a new dynamical systems approach to analyze quintessence models with quadratic potentials, providing global insights into their behavior and observational viability.

Contribution

It introduces a novel regular dynamical system formulation for hilltop quintessence and offers comprehensive global analysis tools for these models.

Findings

Global solution spaces characterized for quadratic potentials

Identification of observationally viable quintessence solutions

Introduction of new monotonic functions for analysis

Abstract

Arguably one can use a canonical scalar field $\varphi$, minimally coupled to gravity, with quadratic potentials $V = \Lambda \pm \frac12 m^2\varphi^2$ to explore some general features of slow-roll and hilltop thawing quintessence, respectively. For each of these two potentials, and pressure-free matter, we introduce a regular unconstrained dynamical system on a compact state space, where the formulation for the hilltop case is new. Together with a derivation of monotonic functions in the two global state space settings, this enables us to obtain global results and to introduce figures that illustrate the global solution spaces of these models, in which we situate the observationally viable quintessence solutions.