Cosmological redshift distortion: deceleration, bias and density parameters from future redshift surveys of galaxies

摘要

The observed two-point correlation functions of galaxies in redshift space become anisotropic due to the geometry of the universe as well as due to the presence of the peculiar velocity field. Expanding the induced anisotropies of the correlation functions with respect to the redshift $z$, we obtain explicit expressions for the deceleration parameter $q_0$, the density parameter 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 $eta_0 equiv Omega_0^{0.6}/b$ from galaxy redshift survey on the basis of a conventional estimator for evolution of the parameter $eta(z)$. 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.