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 cosmo logical 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 mea sure cosmological parameters Omega(0) and b(0) (the bias) or lambda(0) (the cosmological constant) and b(0) is derived by fitting power spec trum moments to the large-scale structure in the linear regime in a wa y 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 ab sence of geometric and evolutionary effects, the ratios of multipole m oments (in particular the zeroth and second) are degenerate for models of constant beta approximate to Omega(0.6)/b(0). However, this degene racy is broken by light-cone effects, so that in principle Omega(0) an d b(0) can be measured separately by a deep enough galaxy redshift sur vey. We find that for surveys of the approximate depth of the SDSS, al l models with Omega(0) less than or equal to 1 are acceptable at the 9 9% confidence limit when a fiducial, open, Omega(0) = 0.3 model is ass umed and bias is unconstrained. At the 95% limit, Omega(0) > 0.85 is r uled out. Furthermore, for this fiducial model, both flat (cosmologica l constant) and open models are expected to reasonably fit the data. F or 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% conf idence limit regardless of the choice of the bias parameter, and open models cannot fit the data even at the 99% confidence limit. We also f ind significant deviations in beta from the naive estimate for both fi ducial models. Thus, we conclude in the case of the SDSS that linear e volution-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 nomi nally excluded unless Omega(0) < 0.3.