Dark Energy from a Phantom Field Near a Local Potential Minimum

Abstract

We examine dark energy models in which a phantom field $\varphi$ is rolling near a local minimum of its potential $V(\varphi )$.We require that $(1/V)(dV/d\varphi )\ll 1$, but $(1/V)(d^{2}V/d{\varphi }^2)$ 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 $(1/V)(d^{2}V/d{\varphi }^2)$ 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, $(1/V)(dV/d\varphi )\ll 1$.

v3: Discussion modified in accordance with referee comments. References added. Results and Conclusions unchanged. v2: Minor typo corrected in Eqn. 16. Results and Conclusions unchanged

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