Slow-Roll Thawing Quintessence

TL;DR

This paper derives slow-roll conditions for thawing quintessence, providing a universal expression for the equation of state parameter w(a) near -1, applicable to general models and matching recent results.

Contribution

It introduces a simplified, two-parameter description of thawing quintessence evolution and derives a universal formula for w(a) that aligns with recent findings.

Findings

Derived a universal expression for w(a) in thawing quintessence.

Identified two key parameters governing the evolution of φ and w.

Established consistency conditions for the approximation |w+1| << 1.

Abstract

We derive slow-roll conditions for thawing quintessence. We solve the equation of motion of $\phi$ for a Taylor expanded potential (up to the quadratic order) in the limit where the equation of state $w$ is close to -1 to derive the equation of state as a function of the scale factor. We find that the evolution of $\phi$ and hence $w$ are described by only two parameters. The expression for $w(a)$, which can be applied to general thawing models, coincides precisely with that derived recently by Dutta and Scherrer for hilltop quintessence. The consistency conditions of $|w+1|\ll 1$ are derived. The slow-roll conditions for freezing quintessence are also derived.