Constraints on a decomposed dark fluid with constant adiabatic sound speed by jointing the geometry test and growth rate after Planck data

In this paper, a unified dark fluid with constant adiabatic sound speed is decomposed into cold dark matter interacting with vacuum energy. Based on a Markov-chain Monte Carlo method, we constrain this model by jointing the geometry and dynamical measurement. The geometry test includes cosmic microwave background radiation from Planck, baryon acoustic oscillation, and type-Ia supernovae; the dynamic measurement is f sigma(8)(z) data points, which is obtained from the growth rate via redshift space distortion, and sigma(8)(z) is the root-mean-square amplitude of the density contrast delta at the comoving 8h(-1) Mpc scale. The jointed constraint shows that alpha = 0.000662(-0.000662)(+0.000173) and alpha = 0.824(-0.0166)(+0.0128). The CMB and matter power spectra are both similar for the case of alpha = mean value and that of alpha = 0. However, the evolutionary curves of f sigma(8)(z) are different. This means that, to some extent, the data points of the growth rate could break the degeneracy of the dark energy models.