The bispectrum of relativistic galaxy number counts

TL;DR

This paper analyzes the relativistic galaxy number counts' bispectrum, identifying new lensing-like contributions that are significant at large redshifts and wide bins, with implications for future cosmological surveys.

Contribution

It introduces the full second-order relativistic bispectrum including new lensing-like terms and provides analytical and numerical evaluations for observational prospects.

Findings

Lensing-like terms significantly affect the bispectrum at large redshifts.

New contributions can dominate the bispectrum in wide redshift bins.

Analytical expressions enable future observational measurements.

Abstract

We discuss the dominant terms of the relativistic galaxy number counts to second order in cosmological perturbation theory on sub-Hubble scales and on intermediate to large redshifts. In particular, we determine their contribution to the bispectrum. In addition to the terms already known from Newtonian second order perturbation theory, we find that there are a series of additional `lensing-like' terms which contribute to the bispectrum. We derive analytical expressions for the full leading order bispectrum and we evaluate it numerically for different configurations, indicating how they can be measured with upcoming surveys. In particular, the new `lensing-like' terms are not negligible for wide redshift bins and even dominate the bispectrum at well separated redshifts. This offers us the possibility to measure them in future surveys.