Thawing quintessence with a nearly flat potential

TL;DR

This paper analyzes thawing quintessence models with nearly flat potentials, deriving a universal relation for the evolution of the equation of state parameter w, which accurately describes the behavior for w close to -1 and is useful for cosmological observations.

Contribution

It derives a universal relation for w(a) in thawing quintessence models under slow-roll conditions, applicable to various potentials and simplifying observational analysis.

Findings

The models converge to a unique relation between 1+w, Omega_phi, and initial conditions.

The derived w(a) expression is accurate within delta w < 0.005 for w < -0.9.

w(a) can be well approximated by a linear function of scale factor a for z < 1.

Abstract

The thawing quintessence model with a nearly flat potential provides a natural mechanism to produce an equation of state parameter, w, close to -1 today. We examine the behavior of such models for the case in which the potential satisfies the slow roll conditions: [(1/V)(dV/dphi)]^2 << 1 and (1/V)(d^2 V/dphi^2) << 1, and we derive the analog of the slow-roll approximation for the case in which both matter and a scalar field contribute to the density. We show that in this limit, all such models converge to a unique relation between 1+w, Omega_phi, and the initial value of (1/V)(dV/dphi). We derive this relation, and use it to determine the corresponding expression for w(a), which depends only on the present-day values for w and Omega_phi. For a variety of potentials, our limiting expression for w(a) is typically accurate to within delta w < 0.005 for w<-0.9. For redshift z < 1, w(a) is well-fit by the Chevallier-Polarski-Linder parametrization, in which w(a) is a linear function of a.