Cosmological Redshift Distortion: Deceleration, Bias, and Density Parameters from Future Redshift Surveys of Galaxies

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Abstract
The observed two-point correlation functions of galaxies in redshift space become anisotropic because of the geometry of the universe, as well as because of the presence of the peculiar velocity field. On the basis of linear perturbation theory, we expand the induced anisotropies of the correlation functions with respect to the redshift z and obtain analytic formulae to infer the deceleration parameter q0, the density parameter Ω0, and the derivative of the bias parameter d ln b/dz at z = 0 in terms of the observable statistical quantities. The present method does not require any assumption of the shape and amplitude of the underlying fluctuation spectrum and thus can be applied to future redshift surveys of galaxies, including the Sloan Digital Sky Survey. We also evaluate quantitatively the systematic error in estimating the value of β0 ≡ Ω00.6/b from a galaxy redshift survey on the basis of a conventional estimator for β0, which neglects both the geometrical distortion effect and the time evolution of the parameter β(z). If the magnitude limit of the survey is as faint as 18.5 (in B band) as in the case of the Sloan Digital Sky Survey, the systematic error ranges between -20% and 10% depending on the cosmological parameters. Although such systematic errors are smaller than the statistical errors in the current surveys, they will definitely dominate the expected statistical error for future surveys.