Sensitivity of redshift distortion measurements to cosmological parameters

The multipole moments of the power spectrum of large-scale structure, observed in redshift space, are calculated for a finite sample volume? incorporating the effects of both the linear velocity field and cosmological geometry. A variance calculation that includes the effects of shot noise is also performed. The sensitivity with which a survey with the depth and geometry of the Sloan Digital Sky Survey (SDSS) can measure cosmological parameters Omega(0) and b(0) (the bias) or lambda(0) (the cosmological constant) and b(0) is derived by fitting power spectrum moments to the large-scale structure in the linear regime in a way that is independent of the evolution of the galaxy number density. A fiducial model is assumed, and the region of parameter space that can then be excluded to a given confidence limit is determined. In the absence of geometric and evolutionary effects, the ratios of multipole moments (in particular the zeroth and second) are degenerate for models of constant beta approximate to Omega(0.6)/b(0). However, this degeneracy is broken by light-cone effects, so that in principle Omega(0) and b(0) can be measured separately by a deep enough galaxy redshift survey. We find that for surveys of the approximate depth of the SDSS, all models with Omega(0) less than or equal to 1 are acceptable at the 99% confidence limit when a fiducial, open, Omega(0) = 0.3 model is assumed and bias is unconstrained. At the 95% limit, Omega(0) > 0.85 is ruled out. Furthermore, for this fiducial model, both flat (cosmological constant) and open models are expected to reasonably fit the data. For flat, cosmological constant models with a fiducial Omega(0) = 0.3, we find that models with Omega(0) > 0.48 are ruled out at the 95% confidence limit regardless of the choice of the bias parameter, and open models cannot fit the data even at the 99% confidence limit. We also find significant deviations in beta from the naive estimate for both fiducial models. Thus, we conclude in the case of the SDSS that linear evolution-free statistics alone can strongly distinguish between Omega(0) =1 and low matter density models only for the fiducial cosmological constant model. For the open model, Omega(0) = 1 is at best only nominally excluded unless Omega(0) < 0.3.