Phantom dark energy models with a nearly flat potential

We examine phantom dark energy models produced by a field with a negative kinetic term and a potential that satisfies the slow-roll conditions: [(1/V)(dV/d phi)](2) << 1 and (1/V)(d(2)V/d phi(2)) << 1. Such models provide a natural mechanism to produce an equation of state parameter, w, slightly less than -1 at present. Using techniques previously applied to quintessence, we show that in this limit, all such phantom models converge to a single expression for w(a), which is a function only of the present-day values of Omega(phi) and w. This expression is identical to the corresponding behavior of w(a) for quintessence models in the same limit. At redshifts z less than or similar to 1, this limiting behavior is well fit by the linear parametrization, w = w(0) + w(a)(1 - a), with w(a) approximate to -1.5(1 + w(0)).