## Redshift-space distortion

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Redshift-space distortions are distortions (stretching and flattening) of the galaxy (2D) two-point correlation function$\xi (\sigma ,\pi )$, and also power spectrum$P(k_{\perp },k_{\parallel })$ (which have to be spherically symmetric in isotropic Universe) caused by peculiar (non-Hubble) motions of galaxies. These distortions can be divided onto:
• Finger of God effect — stretching of $\xi (\sigma ,\pi )$ (or flattening of $P(k_{\perp },k_{\parallel })$) along the line of sight on non-linear (less then $\sim 10\,h^{-1}$ Mpc) scales due to random velocities of galaxies (e.g. virial velocities inside clusters), as far as redshift measurement errors;
• Kaiser effect (or $\beta$-distortion) — flattening of $\xi (\sigma ,\pi )$ (or stretching of $P(k_{\perp },k_{\parallel })$) along the line of sight on linear (more then $\sim 10\,h^{-1}~Mpc$) due to the galaxies infall onto overdense regions.
There is also one more effect causing the distortions of $\xi (\sigma ,\pi )$ and $P(k_{\perp },k_{\parallel })$ even in the real space — the so called geometric flattening.