# The effect of Limber and flat-sky approximations on galaxy weak lensing

## TL;DR

This paper assesses how the Limber and flat-sky approximations affect galaxy weak lensing measurements and concludes their impact on cosmological parameters is negligible for current data, not explaining existing tensions.

## Contribution

It provides a detailed analysis of the approximations' effects on weak lensing data and confirms their minimal influence on cosmological parameter estimation.

## Key findings

- Approximations have negligible impact on current weak lensing cosmological parameters.
- No significant contribution of approximations to the tension between weak lensing and Planck data.
- Validates the use of these approximations for current survey analyses.

## Abstract

We review the effect of the commonly-used Limber and flat-sky approximations on the calculation of shear power spectra and correlation functions for galaxy weak lensing. These approximations are accurate at small scales, but it has been claimed recently that their impact on low multipoles could lead to an increase in the amplitude of the mass fluctuations inferred from surveys such as CFHTLenS, reducing the tension between galaxy weak lensing and the amplitude determined by Planck from observations of the cosmic microwave background. Here, we explore the impact of these approximations on cosmological parameters derived from weak lensing surveys, using the CFHTLenS data as a test case. We conclude that the use of small-angle approximations for cosmological parameter estimation is negligible for current data, and does not contribute to the tension between current weak lensing surveys and Planck.