Redshift-space distortion (RSD) offers an exciting opportunity to test the gravity on cosmological scales. In the presence of galaxy bias, however, the RSD measurement at large scales, where the linear theory prediction is safely applied, is known to exhibit a degeneracy between the parameters of structure growth $f$ and fluctuation amplitude ${\sigma }_8$, and one can only constrain the parameters in the form of $f{\sigma }_8$. In order to disentangle this degeneracy, in this paper, we go beyond the linear theory and consider the model of RSD applicable to a weakly nonlinear regime. Based on the Fisher matrix analysis, we show explicitly that the degeneracy of the parameter $f{\sigma }_8$ can be broken, and ${\sigma }_8$ is separately estimated in the presence of galaxy bias. Performing further the Markov chain Monte Carlo analysis, we verify that our model correctly reproduces the fiducial values of $f{\sigma }_8$ and ${\sigma }_8$, with the statistical errors consistent with those estimated from the Fisher matrix analysis. We show that upcoming galaxy survey of the stage-IV class can unambiguously determine ${\sigma }_8$ at the precision down to less than or approximately equal to 10% at higher redshifts even if we restrict the accessible scales to $k\lesssim 0.16h{\mathrm{Mpc}}^{-1}$.

• Received 16 February 2021
• Accepted 14 July 2021

DOI:https://doi.org/10.1103/PhysRevD.104.043528