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 spacebecome anisotropic due to the geometry of the universe as well as due to thepresence of the peculiar velocity field. On the basis of linear perturbationtheory, we expand the induced anisotropies of the correlation functions withrespect to the redshift $z$, and obtain analytic formulae to infer thedeceleration parameter $q_0$, the density parameter $Omega_0$ and thederivative of the bias parameter $dln b/dz$ at $z=0$ in terms of theobservable statistical quantities. The present method does not require anyassumption of the shape and amplitude of the underlying fluctuation spectrum,and thus can be applied to future redshift surveys of galaxies including theSloan Digital Sky Survey. We also evaluate quantitatively the systematic errorin estimating the value of $eta_0 equiv Omega_0^{0.6}/b$ from a galaxyredshift survey on the basis of a conventional estimator for $eta_0$ whichneglects both the geometrical distortion effect and the time evolution of theparameter $eta(z)$. 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 systematicerror ranges between -20% and 10% depending on the cosmological parameters.Although such systematic errors are smaller than the statistical errors in thecurrent surveys, they will dominate the expected statistical error for futuresurveys.