What galaxy surveys really measure

Abstract

In this paper we compute the quantity which is truly measured in a large galaxy survey. We take into account the effects coming from the fact that we actually observe galaxy redshifts and sky positions and not true spatial positions. Our calculations are done within linear perturbation theory for both the metric and the observer velocities but they can be used for non-linear matter power spectra. We shall see that the complications due to the fact that we only observe on our background lightcone and that we do not truly know the distance of the observed galaxy, but only its redshift is not only an additional difficulty, but even more a new opportunity for future galaxy surveys.Comment: 16 pages, 11 figures; v2: 1 table and 4 figures added showing the ratio between the new contributions and the total angular power spectrum. Accepted for publication in PRD. v3: sign typo corrected in eq. (31