Redshift weighted galaxy number counts

TL;DR

This paper introduces the redshift fluctuation as a new, gauge-invariant cosmological observable that captures smaller scale radial modes than traditional galaxy number counts, with potential applications in future spectroscopic surveys.

Contribution

It provides a fully relativistic expression for the redshift fluctuation and analyzes its angular power spectrum, highlighting its differences from standard galaxy number count fluctuations.

Findings

Redshift fluctuation effectively captures smaller radial modes.

Relativistic contributions significantly affect the angular power spectrum.

Forecasts show potential for improved cosmological measurements in future surveys.

Abstract

In this paper we introduce the `redshift fluctuation' as a gauge-invariant cosmological observable and give its fully relativistic expression at first order in cosmological perturbation theory. We show that this corresponds effectively to number counts with a radial window function with vanishing mean which therefore resolve smaller scale radial modes than standard number counts. In a detailed analysis of the angular power spectrum of this new variable, we study the relevance of different relativistic contributions, and how it differs from the conventional observable galaxy number count fluctuations. In order to investigate its utility for future spectroscopic surveys, we perform Fisher forecasts for a Euclid-like and an SKAII-like configuration, as examples. Particular focus is placed on the dependence of the results on the size of the redshift bins and on the cutoff in $\ell$ adopted in the analysis.