Classifying the behavior of noncanonical quintessence

TL;DR

This paper analyzes the stability and behavior of noncanonical quintessence models with power-law and exponential potentials, revealing their limited suitability for dark energy and characterizing their evolution and oscillatory solutions.

Contribution

It derives general stability conditions for noncanonical quintessence with specific potentials and explores their dynamical behaviors, including thawing solutions and oscillations.

Findings

Most noncanonical quintessence models do not produce viable dark energy.

Scaling solutions are often not attractors, leading to zero-potential-like behavior.

Distinct evolution of the equation of state parameter w(a) compared to canonical models.

Abstract

We derive general conditions for the existence of stable scaling solutions for the evolution of noncanonical quintessence, with a Lagrangian of the form $\mathcal{L}(X,\phi)=X^{\alpha}-V(\phi)$, for power-law and exponential potentials when the expansion is dominated by a background barotropic fluid. Our results suggest that in most cases, noncanonical quintessence with such potentials does not yield interesting models for the observed dark energy. When the scaling solution is not an attractor, there is a wide range of model parameters for which the evolution asymptotically resembles a zero-potential solution with equation of state parameter $w = 1/(2\alpha -1)$, and oscillatory solutions are also possible for positive power-law potentials; we derive the conditions on the model parameters which produce both types of behavior. We investigate thawing noncanonical models with a nearly-flat potential and derive approximate expressions for the evolution of $w(a)$. These forms for $w(a)$ differ in a characteristic way from the corresponding expressions for canonical quintessence.