Revisiting CFHTLenS cosmic shear: optimal E/B mode decomposition using COSEBIs and compressed COSEBIs

We present a re-analysis of the CFHTLenS weak gravitational lensing survey using Complete Orthogonal Sets of E/B-mode Integrals, known as COSEBIs. COSEBIs provide a complete set of functions to efficiently separate E-modes from B-modes and hence allow for robust and stringent tests for systematic errors in the data. This analysis reveals significant B-modes on large angular scales that were not previously seen using the standard E/B decomposition analyses. We find that the significance of the B-modes is enhanced when the data are split by galaxy type and analysed in tomographic redshift bins. Adding tomographic bins to the analysis increases the number of COSEBIs modes, which results in a less-accurate estimation of the covariance matrix from a set of simulations. We therefore also present the first compressed COSEBIs analysis of survey data, where the COSEBIs modes are optimally combined based on their sensitivity to cosmological parameters. In this tomographic CCOSEBIs analysis, we find the B-modes to be consistent with zero when the full range of angular scales are considered.