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Based on the cosmic shear data from the Canada-France-Hawaii TelescopeLensing Survey (CFHTLenS), Kilbinger et al. (2013) obtained a constraint on theamplitude of matter fluctuations of$\sigma_8({\Omega_\mathrm{m}}/0.27)^{0.6}=0.79\pm0.03$ from the two-pointcorrelation 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 thepower spectrum, and performing a different analysis, Liu et al. (2015) obtainedthe higher value of$\sigma_8({\Omega_\mathrm{m}}/0.27)^{0.64}=0.87^{+0.05}_{-0.06}$. We hereinvestigate the origin of this difference, by performing a fair side-by-sidecomparison of the 2PCF and power spectrum analyses on CFHTLenS data. We findthat these two statistics indeed deliver different results, even when appliedto the same data in an otherwise identical procedure. We identify excess powerin the data on small scales ($\ell>5,000$) driving the larger values inferredfrom the power spectrum. We speculate on the possible origin of this excesssmall-scale power. More generally, our results highlight the utility ofanalysing the 2PCF and the power spectrum in tandem, to discover (and to helpcontrol) systematic errors.

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