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 subdominant. At late times, when rho(phi) becomes comparable to the matter density rho(m), 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 surprisingly accurate even down to z=0. We find that w and Omega(phi) are related linearly to first order, and derive a semianalytic 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.