# The matter fluctuation amplitude inferred from the weak lensing power spectrum and correlation function in CFHTLenS data

## TL;DR

This study compares matter fluctuation amplitude estimates from CFHTLenS weak lensing data using two different statistical methods, revealing discrepancies due to small-scale excess power and emphasizing the importance of combined analysis.

## Contribution

It provides a side-by-side comparison of 2PCF and power spectrum analyses on the same data, identifying sources of differences and systematic errors.

## Key findings

- Different results from 2PCF and power spectrum analyses on the same data.
- Excess small-scale power influences the higher amplitude inferred from the power spectrum.
- Highlighting the importance of joint analysis to identify systematic errors.

## Abstract

Based on the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), Kilbinger et al. (2013) obtained a constraint on the amplitude of matter fluctuations of $\sigma_8({\Omega_\mathrm{m}}/0.27)^{0.6}=0.79\pm0.03$ from the two-point correlation function (2PCF). This is $\approx3\sigma$ lower than the value $0.89\pm0.01$ derived from Planck data on cosmic microwave background (CMB) anisotropies. On the other hand, based on the same CFHTLenS data, but using the power spectrum, and performing a different analysis, Liu et al. (2015) obtained the higher value of $\sigma_8({\Omega_\mathrm{m}}/0.27)^{0.64}=0.87^{+0.05}_{-0.06}$. We here investigate the origin of this difference, by performing a fair side-by-side comparison of the 2PCF and power spectrum analyses on CFHTLenS data. We find that these two statistics indeed deliver different results, even when applied to the same data in an otherwise identical procedure. We identify excess power in the data on small scales ($\ell>5,000$) driving the larger values inferred from the power spectrum. We speculate on the possible origin of this excess small-scale power. More generally, our results highlight the utility of analysing the 2PCF and the power spectrum in tandem, to discover (and to help control) systematic errors.