Dark Energy from a Phantom Field Near a Local Potential Minimum

TL;DR

This paper develops a general analytical framework for modeling dark energy using a phantom field near a potential minimum, accurately predicting the equation of state parameter w over cosmic time.

Contribution

It derives a universal expression for w(a) in phantom models near a potential minimum, extending hilltop quintessence techniques and matching numerical results within 1%.

Findings

Derived a general formula for w(a) in phantom models.

The formula closely matches numerical solutions within 1%.

Reduces to known slow-roll results in flat potential limit.

Abstract

We examine dark energy models in which a phantom field $\phi$ is rolling near a local minimum of its potential $V(\phi)$.We require that $(1/V)(dV/d\phi) \ll 1$, but $(1/V)(d^2 V/d\phi^2)$ can be large. Using techniques developed in the context of hilltop quintessence, we derive a general expression for $w$ as a function of the scale factor, and as in the hilltop case, we find that the dynamics of the field depend on the value of $(1/V)(d^2 V/d\phi^2)$ near the mimimum. Our general result gives a value for $w$ that is within 1% of the true (numerically-derived) value for all of the particular cases examined. Our expression for $w(a)$ reduces to the previously-derived phantom slow-roll result of Sen and Scherrer in the limit where the potential is flat, $(1/V)(dV/d\phi) \ll 1$.