Measuring the lensing potential with tomographic galaxy number counts

TL;DR

This paper forecasts how future galaxy surveys can tomographically measure the lensing potential using galaxy number counts, providing an independent test of cosmological models and gravity theories.

Contribution

It introduces a Fisher matrix forecast method for measuring the lensing potential from galaxy counts in future surveys, including a new fitting formula for magnification bias.

Findings

Cross-bin correlations are highly sensitive to the lensing potential.

Surveys can measure the lensing potential amplitude with precision comparable to other cosmological parameters.

The method offers an independent test of the standard cosmological model.

Abstract

We investigate how the lensing potential can be measured tomographically with future galaxy surveys using their number counts. Such a measurement is an independent test of the standard $\Lambda$CDM framework and can be used to discern modified theories of gravity. We perform a Fisher matrix forecast based on galaxy angular-redshift power spectra, assuming specifications consistent with future photometric Euclid-like surveys and spectroscopic SKA-like surveys. For the Euclid-like survey we derive a fitting formula for the magnification bias. Our analysis suggests that the cross correlation between different redshift bins is very sensitive to the lensing potential such that the survey can measure the amplitude of the lensing potential at the same level of precision as other standard $\Lambda$CDM cosmological parameters.