Weak lensing deflection of three-point correlation functions

TL;DR

This paper derives a general expression for weak lensing deflection effects on three-point correlation functions, showing that the impact is small and likely undetectable in upcoming surveys.

Contribution

It provides a novel, general formula for lensing deflection effects on any three-point statistic in cosmology.

Findings

Deflection effects are largest around redshift z=2.

Lensing smooths out BAO peaks, reducing peak-to-trough contrast.

Impact is at the percent level, below detection thresholds for Euclid-like surveys.

Abstract

Weak gravitational lensing alters the apparent separations between observed sources, potentially affecting clustering statistics. We derive a general expression for the lensing deflection which is valid for any three-point statistic, and investigate its effect on the three-point clustering correlation function. We find that deflection of the clustering correlation function is greatest at around $z=2$. It is most prominent in regions where the correlation function varies rapidly, in particular at the baryon acoustic oscillation scale where it smooths out the peaks and troughs, reducing the peak-to-trough difference by about 0.1 percent at $z=1$ and around 2.3 percent at $z=10$. The modification due to lensing deflection is typically at the per cent level of the expected errors in a Euclid-like survey and therefore undetectable.