Isolating relativistic effects in large-scale structure

TL;DR

This paper develops a fully relativistic framework for analyzing galaxy number counts, highlighting how inhomogeneities distort observations and proposing methods to isolate relativistic effects like Doppler and gravitational redshift in large-scale structure data.

Contribution

It provides a comprehensive relativistic calculation of galaxy counts and introduces techniques to isolate specific relativistic effects in observational data.

Findings

Relativistic effects significantly impact large-scale galaxy observations.

The two-point correlation function can effectively isolate relativistic effects.

Doppler and gravitational redshift effects can be identified via dipole signals in galaxy cross-correlations.

Abstract

We present a fully relativistic calculation of the observed galaxy number counts in the linear regime. We show that besides the density fluctuations and redshift-space distortions, various relativistic effects contribute to observations at large scales. These effects all have the same physical origin: they result from the fact that our coordinate system, namely the galaxy redshift and the incoming photons' direction, is distorted by inhomogeneities in our universe. We then discuss the impact of the relativistic effects on the angular power spectrum and on the two-point correlation function in configuration space. We show that the latter is very well adapted to isolate the relativistic effects since it naturally makes use of the symmetries of the different contributions. In particular, we discuss how the Doppler effect and the gravitational redshift distortions can be isolated by looking for a dipole in the cross-correlation function between a bright and a faint population of galaxies.