Dark energy from a phantom field near a local potential minimum

We examine dark energy models in which a phantom field ϕ is rolling near a local minimum of its potential V(ϕ). We require that (1/V)(dV/dϕ)≪1, but (1/V)(d2V/dϕ2) 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)(d2V/dϕ2) near the minimum. 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/dϕ)≪1.