  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.
