The growth rate of matter density perturbations has been measured from redshift-space distortion (RSD) in the galaxy power spectrum. We constrain the model parameter space for representative modified gravity models to explain the dark energy problem, by using the recent data of $f_m(z){\sigma }_8(z)$ at the redshifts $z=0.06–0.8$ measured by WiggleZ, SDSS LRG, BOSS, and 6dFGRS. We first test the Hu-Sawicki’s $f(R)$ dark energy model, and find that only the parameter region close to the standard $\Lambda$ cold dark matter model is allowed ($\lambda >12$ and 5 for $n=1.5$ and 2, respectively, at 95% C.L.). We then investigate the covariant Galileon model with a de Sitter attractor and show that the parameter space consistent with the background expansion history is excluded by the RSD data at more than $8\sigma$ because of the too large growth rate predicted by the theory. Finally, we consider the extended Galileon scenario, and we find that, in contrast to the covariant Galileon, there is a model parameter space for a tracker solution that is consistent with the RSD data within a $2\sigma$ level.

• Received 23 August 2012

DOI:https://doi.org/10.1103/PhysRevD.87.103002