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) ^21 and (1/V) (d^2V/d^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 _ and w. This expression is identical to the corresponding behavior of w (a) for quintessence models in the same limit. At redshifts z1, this limiting behavior is well fit by the linear parametrization, w=w₀+w₀ (1-a), with w₀-1. 5 (1+w₀).