Self-calibration and robust propagation of photometric redshift distribution uncertainties in weak gravitational lensing

We present a method that accurately propagates residual uncertainties in photometric redshift distributions into the cosmological inference from weak lensing measurements. The redshift distributions of tomographic redshift bins are parameterised using a flexible modified Gaussian mixture model. We fit this model to pre-calibrated redshift distributions and implement an analytic marginalisation over the potentially several hundred redshift nuisance parameters in the weak lensing likelihood, which is demonstrated to accurately recover the cosmological posterior. By iteratively fitting cosmological and nuisance parameters arising from the redshift distribution model, we perform a self-calibration of the redshift distributions via the tomographic cosmic shear measurements. Our method is applied to KV450 data, which comprises a combination of the third data release of the Kilo-Degree Survey and the VISTA Kilo-Degree Infrared Galaxy Survey. We find constraints on cosmological parameters that are in very good agreement with the fiducial KV450 cosmic shear analysis and investigate the effects of the more flexible model on the self-calibrated redshift distributions. We observe posterior shifts in the medians of the five tomographic redshift distributions of up to Δz ≈ 0.02, which are, however, degenerate with an observed decrease in the amplitude of intrinsic galaxy alignments of about 10%