Constraints on the dark matter equation of state with redshift-space distortion

In this paper, we study a model which is composed by the cosmological constant and dark matter with nonzero equation of state parameter, which could be called as $\Lambda$wDM. In the synchronous gauge, we obtain the perturbation equations of dark matter, and deduce the evolution equations of growth factor about the dark matter and baryons. Based on the Markov Chain Monte Carlo method, we constrain this model by the recently available cosmic observations which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and $f\sigma_8(z)$ data points from redshift-space distortion. The results present a tighter constraint on the model than the case without $f\sigma_8(z)$ data. In 3$\sigma$ regions, we find the dark matter equation of state parameter $w_{dm}$=$0.000111_{- 0.000701-0.00137-0.00180}^{+0.000688+0.00136+0.00181}$. After an extra model parameter $w_{dm}$ is considered, the difference between the minimum values of $\chi^2$ of our model and standard model is $\Delta\chi^2_{min}=0.598$. Although the currently available cosmic observations mildly favor the nonzero dark matter equation of state parameter, no significant deviation from the $\Lambda$CDM model is found in 1$\sigma$ region.