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The growth index $\gamma_L$ was proposed to investigate the possibledeviation from the standard $\Lambda$CDM model and Einstein's gravity theory ina dynamical perspective. Recently, thanks to the measurement of the cosmicgrowth rate via the redshift-space distortion, one can understand the evolutionof density contrast through $f\sigma_8(z)$, where $f(z)=d\ln \delta/d \ln a$ isthe growth rate of matter and $\sigma_8(z)$ is the rms amplitude of the densitycontrast $\delta$ at the comoving $8h^{-1}$ Mpc scale. In this paper, we usethe redshift space distortion data points to study the growth index on thebases of Einstein's gravity theory and a modified gravity theory under theassumption of $f=\Omega_m(a)^{\gamma_L}$. The cosmic background evolution isfixed by the cosmic observations from the type Ia supernovae SNLS3, cosmicmicrowave background radiation data from {\it Planck} and baryon acousticoscillations. Via the Markov Chain Monte Carlo method, we found the $\gamma_L$values for Einstein's gravity with a cosmological constant, $w=constant$ darkenergy and a modified gravity theory in the $1,2,3\sigma$ regions respectively:$0.675_{-0.0662-0.120-0.155}^{+0.0611+0.129+0.178}$,$0.745_{-0.0819-0.146-0.190}^{+0.0755+0.157+0.205}$ and$0.555_{-0.0167-0.0373-0.0516}^{+0.0193+0.0335+0.0436}$. In the Einstein'sgravity theory, the values of growth index $\gamma_L$ show almost $2\sigma$deviation from the theoretical prediction 6/11 for the $\Lambda$CDM model.However in the modified gravity framework, a deviation from the Einstein'srelativity is not detected in $1\sigma$ region. That implies that the currentlyavailable cosmic observations don't expect an alternative modified gravitytheory beyond the $\Lambda$CDM model under Einstein's gravity, but that thesimple assumption of $f=\Omega_m^{\gamma_L}$ should be improved.

Growth Index after the Planck Results