Testing for dynamical dark energy models with redshift-space distortions

The red-shift space distortions in the galaxy power spectrum can be used to measure the growth rate of matter density perturbations δ_m. For dynamical dark energy models in General Relativity we provide a convenient analytic formula of f(z)σ₈ (z) written as a function of the redshift z, where f = dln δ_m/dln a (a is the cosmological scale factor) and σ₈ is the rms amplitude of over-density at the scale 8 h^-1 Mpc. Our formula can be applied to the models of imperfect fluids, quintessence, and k-essence, provided that the dark energy equation of state w does not vary significantly and that the sound speed is not much smaller than 1. We also place observational constraints on dark energy models of constant w and tracking quintessence from the recent data of red-shift space distortions.