Going beyond the Kaiser redshift-space distortion formula: A full general relativistic account of the effects and their detectability in galaxy clustering

Abstract

The proper general relativistic description of the observed galaxy power spectrum is substantially different from the standard Newtonian description on large scales, providing a unique opportunity to test general relativity on horizon scales. Using the Einstein equations, the general relativistic effects can be classified as two new terms that represent the velocity and the gravitational potential, coupling to the time evolution of galaxy number density and Hubble parameter. Compared to the dominant density and velocity redshift-space distortion terms, the former scales as H/k and correlates the real and imaginary parts of the Fourier modes, while the latter scales as (H/k)^2, where k is the comoving wave number and H is the conformal Hubble parameter. We use the recently developed methods to reduce the sampling variance and shot noise to show that in an all sky galaxy redshift survey at low redshift the velocity term can be measured at 10-sigma confidence level, if one can utilize halos of mass M>10^{10} Msun, while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect the primordial non-Gaussianity is little compromised.