Slow-roll Extended Quintessence

TL;DR

This paper derives slow-roll conditions for a non-minimally coupled scalar field during radiation and matter domination, revealing unique dynamical ratios and asymptotic behaviors distinct from minimally coupled quintessence.

Contribution

It extends previous slow-roll analyses to non-minimally coupled scalar fields, providing new conditions and insights into their cosmological evolution.

Findings

The ratio $rac{oxed{ ext{d}^2 ext{ extphi}}{ ext{d}t^2}}{3Hrac{ ext{d} ext{ extphi}}{ ext{d}t}}$ becomes constant and negative.

The scalar field's equation of state approaches that of minimally coupled thawing quintessence.

Distinct dynamical behavior compared to minimally coupled scalar fields.

Abstract

We derive the slow-roll conditions for a non-minimally coupled scalar field (extended quintessence) during the radiation/matter dominated era extending our previous results for thawing quintessence. We find that the ratio $\ddot\phi/3H\dot\phi$ becomes constant but negative, in sharp contrast to the ratio for the minimally coupled scalar field. We also find that the functional form of the equation of state of the scalar field asymptotically approaches that of the minimally coupled thawing quintessence.