Hilltop Quintessence

TL;DR

This paper derives a general analytical expression for the evolution of the dark energy equation of state in hilltop quintessence models, showing high accuracy across various potentials and extending previous slow-roll results.

Contribution

It provides a new, general solution for w(a) in hilltop quintessence models, applicable to different potential curvatures and improving upon prior specific cases.

Findings

Derived an accurate analytical expression for w(a) near a potential maximum.

Validated the solution against specific models with less than 0.5% deviation.

Extended slow-roll results to cases with non-zero potential curvature.

Abstract

We examine hilltop quintessence models, in which the scalar field is rolling near a local maximum in the potential, and w is close to -1. We first derive a general equation for the evolution of the scalar field in the limit where w is close to -1. We solve this equation for the case of hilltop quintessence to derive w as a function of the scale factor; these solutions depend on the curvature of the potential near its maximum. Our general result is in excellent agreement (delta w < 0.5%) with all of the particular cases examined. It works particularly well (delta w < 0.1%) for the pseudo-Nambu-Goldstone Boson potential. Our expression for w(a) reduces to the previously-derived slow-roll result of Sen and Scherrer in the limit where the curvature goes to zero. Except for this limiting case, w(a) is poorly fit by linear evolution in a.