Clustering statistics on a light-cone in the cosmological redshift space

We summarize a series of our recent work concerning the cosmological redshift-space distortion and light-cone effects. After briefly describing the theoretical formalism, we show how those effects are sensitive to the cosmological parameters. Then we apply this formalism to predict the two-point correlation functions and power spectra for the X-ray clusters, galaxies and quasars in future surveys, and discuss their cosmological implications. 1. Cosmological effects in the high-z universe Redshift surveys of galaxies definitely serve as the central database for observational cosmology. In addition to the existing catalogues including CfA1, CfA2, SSRS, and the Las Campanas survey, upcoming galaxy surveys such as 2dF (2-degree Field Survey) and SDSS (Sloan Digital Sky Survey) are expected to provide important clues to the evolution of structure in the universe. In addition to those shallower surveys, clustering in the universe in the range z = 1− 3 has been partially revealed by, for instance, the Lyman-break galaxies and X-ray selected AGNs. In particular, the 2dF and SDSS QSO redshift surveys promise to extend the observable scale of the universe by an order of magnitude, up to a few Gpc. A proper interpretation of such redshift surveys in terms of the clustering evolution, however, requires an understanding of many cosmological effects which can be neglected for z ≪ 1 and thus have not been considered seriously so far. These cosmological contaminations include linear redshift-space (velocity) distortion (Kaiser 1987), nonlinear redshift-space (velocity) distortion (e.g., Suto & Suginohara 1991; Cole, Fisher, & Weinberg 1994), cosmological redshift-space (geometrical) distortion (Alcock & Paczyński 1979; Ballinger, Peacock, & Heavens 1996; Matsubara & Suto 1996), and cosmological light-cone effect (Yamamoto