Clustering in redshift space: Linear theory

The clustering in redshift space is studied here to first order within the framework of gravitational instability. The distortion introduced by the peculiar velocities of galaxies results in anisotropy in the galaxy distribution and mode-mode coupling when analyzed in Fourier space. An exact linear calculation of the full covariance matrix in both real and Fourier space is presented here. The explicit dependence on Ω₀ and the biasing parameter is calculated, and its potential use as a probe of these parameters is discussed. Kaiser's formalism, which is valid in the small-angle approximation, is extended here to the general case, including all-sky surveys. The covariance matrix in real space is calculated explicitly for the cold dark matter model, where the behavior along and perpendicular to the line of sight is shown.