Toward a more stringent test of gravity with the redshift space power spectrum: Simultaneous probe of growth and amplitude of large-scale structure

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 less than or similar to 0.16 h Mpc(-1).