What galaxy surveys really measure

TL;DR

This paper clarifies the actual measurements in galaxy surveys by accounting for observational effects like redshifts and sky positions, highlighting both challenges and opportunities for future cosmological studies.

Contribution

It provides a detailed calculation of the true measured quantity in galaxy surveys, incorporating observational effects within linear perturbation theory.

Findings

Observed quantities differ from true spatial positions due to redshift and sky position effects.

The complications from observing on the lightcone and redshift uncertainties are both challenges and opportunities.

The methodology can be extended to non-linear matter power spectra.

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.