The Evolution of Inverse Power Law Quintessence at Low Redshift

Quintessence models based on a scalar field, phi, with an inverse power law potential display simple tracking behavior at early times, when the quintessence energy density, rho_phi, is sub-dominant. At late times, when rho_phi becomes comparable to the matter density, the evolution of phi diverges from its scaling behavior. We calculate the first order departure of phi from its tracker solution at low redshift. Our results for the evolution of phi, rho_phi, Omega_phi, and w are suprisingly accurate even down to z=0. We find that w and Omega_phi are related linearly to first order. We also derive a semi-analytic expression for w(z) which is accurate to within a few percent. Our analytic techniques are potentially applicable to any quintessence model in which the quintessence component comes to dominate at late times.