Isodensity statistics on clustering of high-z objects in cosmological redshift spaces

We discuss the systematic effects arising from the cosmological redshift sp ace (geometric) distortion on the statistical analysis of the isodensity co ntour using high-redshift catalogs. In particular, we present a simple theo retical model for isodensity statistics in cosmological redshift space, as a generalization of earlier work by Matsubara. The statistical quantities c onsidered here are the two- and three-dimensional genus of the isodensity c ontour, the surface area, the length of the contour intersecting with a pla ne, and the number of crossing points of the isodensity contour on a line. We give useful analytic formulae for the isodensity statistics, which take into account corrections from the geometric distortion, the nonlinear clust ering, and the nonlinear velocity distortion phenomenologically. We then de monstrate how the geometric distortion and the nonlinear corrections alter the shapes of the statistical quantities on the basis of plausible cosmolog ical models. Our results show that the nonlinear correction can be sensitiv e to a choice of the redshift-space coordinate as increasing the redshift. The low-dimensional quantities, such as the two-dimensional genus, systemat ically yield anisotropy due to the geometric and velocity distortions, and their angle-dependence shows a 10%-20% difference of amplitude. Sensitiviti es for typical high-redshift samples are estimated in an analytic manner, a nd the influence of the light-cone effect for the isodensity statistics is also discussed. A simple estimation suggests that the systematic effects of geometric and redshift-space distortions can become comparable to or even dominate the statistical error of deep cluster samples and future high-reds hift galaxy surveys. These systematic effects might be a useful tool in pro bing the cosmological model of our universe.