Generalized shear-ratio tests: A new relation between cosmological distances, and a diagnostic for a redshift-dependent multiplicative bias in shear measurements

TL;DR

This paper introduces a new, model-independent relation between cosmological distances and shear ratios in weak lensing, providing a diagnostic tool to detect redshift-dependent biases in shear measurements for upcoming surveys.

Contribution

It derives a novel, bias-independent relation between shear ratios at different redshifts, enabling systematic error detection in weak lensing data analysis.

Findings

Derived a new relation between cosmological distances valid in isotropic space-times.

Proposed generalized shear-ratio tests to identify redshift-dependent shear biases.

Provided a method to test for systematics in future weak lensing surveys.

Abstract

We derive a new relation between cosological distances, valid in any (statistically) isotropic space-time and independent of cosmological parameters or even the validity of the field equation of General Relativity. In particular, this relation yields an equation between those distance ratios which are the geometrical factors determining the strength of the gravitational lensing effect of mass concentrations. Considering a combination of weak lensing shear ratios, based on lenses at two different redshifts, and sources at three different redshifts, we derive a relation between shear-ratio tests which must be identically satisfied. A redshift-dependent multiplicative bias in shear estimates will violate this relation, and thus can be probed by this generalized shear-ratio test. Combining the lensing effect for lenses at three different redshifts and three different source redshifts, a relation between shear ratios is derived which must be valid independent of a multiplicative bias. We propose these generalized shear-ratio tests as a diagnostic for the presence of systematics in upcoming weak lensing surveys.