Discrepancies between CFHTLenS cosmic shear & Planck: new physics or systematic effects?

There is currently a discrepancy in the measured value of the amplitude of matter clustering, parameterised using $\sigma_8$, inferred from galaxy weak lensing, and cosmic microwave background data, which could be an indication of new physics, such as massive neutrinos or a modification to the gravity law, or baryon feedback. In this paper we make the assumption that the cosmological parameters are well determined by Planck, and use weak lensing data to investigate the implications for baryon feedback and massive neutrinos, as well as possible contributions from intrinsic alignments and biases in photometric redshifts. We apply a non-parametric approach to model the baryonic feedback on the dark matter clustering, which is flexible enough to reproduce the OWLS and Illustris simulation results. The statistic we use, 3D cosmic shear, is a method that extracts cosmological information from weak lensing data using a spherical-Bessel function power spectrum approach. We analyse the CFHTLenS weak lensing data and, assuming best fit cosmological parameters from the Planck CMB experiment, find that there is no evidence for baryonic feedback on the dark matter power spectrum, but there is evidence for a bias in the photometric redshifts in the CFHTLenS data, consistent with a completely independent analysis by Choi et al. (2015), based on spectroscopic redshifts; and that these conclusions are robust to assumptions about the intrinsic alignment systematic. We also find an upper limit on the sum of neutrino masses conditional on other $\Lambda$CDM parameters being fixed, of $< 0.28$ eV ($1\sigma$).