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