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/dphi)]^2 << 1 and (1/V)(d^2 V/dphi^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 < 1, this limiting behavior is well fit by the linear parametrization, w=w_0 + w_a(1-a), with w_a \approx -1.5(1+w_0).