Sensitivity of Redshift Distortion Measurements to Cosmological Parameters

Abstract

The multipole moments of the power spectrum of large scale structure, observed in redshift space, are calculated for a finite sample volume including the effects of both the linear velocity field and geometry. A variance calculation is also performed including the effects of shot noise. The sensitivity with which a survey with the depth and geometry of the Sloan Digital Sky Survey (SDSS) can measure cosmological parameters $Ω_0$ and $b_0$ (the bias) or $λ_0$ (the cosmological constant) and $b_0$ is derived through fitting power spectrum moments to the large scale structure in the linear regime in a way which is independent of the evolution of the galaxy number density. We find that for surveys of the approximate depth of the SDSS no restrictions can be placed on $Ω_0$ at the 99% confidence limit when a fiducial open, $Ω_0 = 0.3 $ model is assumed and bias is unconstrained. At the 95% limit, $Ω_{0} < .85$ 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 $Ω_{0} = 0.3$, we find that models with $Ω_{0} > 0.48$ 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 correct an error which which caused us to overestimate the cosmic variance of our statistics. We also include shot noise in the new variace calculation. In our fitting proceedure, we now include $σ$, the non-linear velocity dispersion, as a free parameter. Our conclusions are modifed as a result, with $Ω_0=0.3$ open models now nominaly excluding $Ω_0 = 1$ at the 95% but not 99% confidence limit