General Relativistic corrections in density-shear correlations

TL;DR

Relativistic light-cone effects significantly impact galaxy-galaxy lensing measurements, especially at high redshifts, necessitating their inclusion for accurate cosmological analyses.

Contribution

This paper quantifies the magnitude of relativistic corrections in density-shear correlations and emphasizes their importance in future high-redshift surveys.

Findings

Relativistic corrections can cause up to 50% systematic errors in high-redshift bins.

Lensing of the counted source populations by intervening masses is a dominant correction.

Corrections become increasingly significant at higher redshifts and larger scales.

Abstract

We investigate the corrections which relativistic light-cone computations induce on the correlation of the tangential shear with galaxy number counts, also known as galaxy-galaxy lensing. The standard-approach to galaxy-galaxy lensing treats the number density of sources in a foreground bin as observable, whereas it is in reality unobservable due to the presence of relativistic corrections. We find that already in the redshift range covered by the DES first year data, these currently neglected relativistic terms lead to a systematic correction of up to 50% in the density-shear correlation function for the highest redshift bins. This correction is dominated by the the fact that a redshift bin of number counts does not only lens sources in a background bin, but is itself again lensed by all masses between the observer and the counted source population. Relativistic corrections are currently ignored in the standard galaxy-galaxy analyses, and the additional lensing of a counted source populations is only included in the error budget (via the covariance matrix). At increasingly higher redshifts and larger scales, these relativistic and lensing corrections become however increasingly more important, and we here argue that it is then more efficient, and also cleaner, to account for these corrections in the density-shear correlations.