Attractor solutions for general hessence dark energy

TL;DR

This paper analyzes the critical points of the hessence dark energy model with general potentials and interactions, revealing stable late-time attractors and new solutions with finite field values and potential-dependent stabilities.

Contribution

It provides a comprehensive analysis of the critical points for the hessence model, including new solutions with finite field values and stability criteria based on the potential's second derivative.

Findings

Existence of stable late-time attractors in general hessence models.

Identification of new solutions with finite hessence field values.

Stability depends on the second derivative of the potential.

Abstract

As a candidate for the dark energy, the hessence model has been recently introduced. We discuss the critical points of this model in almost general case, that is for arbitrary hessence potential and almost arbitrary hessence-background matter interaction. It is shown that in all models, there always exist some stable late-time attractors. It is shown that our general results coincide with those solutions obtained earlier for special cases, but some of them are new. These new solutions have two unique characteristics. First the hessence field has finite value in these solutions and second, their stabilities depend on the second derivative of the hessence potential.