Enhancing cosmic shear with the multiscale lensing probability density function

We quantify the cosmological constraining power of the 'lensing probability density function (PDF)' - the one-point probability density of weak lensing convergence maps - by modelling this statistic numerically with an emulator trained on w cold dark matter cosmic shear simulations. After validating our methods on Gaussian and lognormal fields, we show that 'multiscale' PDFs - measured from maps with multiple levels of smoothing - offer considerable gains over two-point statistics, owing to their ability to extract non-Gaussian information: For a mock Stage-III survey, lensing PDFs yield 33 per cent tighter constraints on the clustering parameter $S_8=\sigma _8\sqrt{\Omega _{\rm m}/0.3}$ than the two-point shear correlation functions. For Stage-IV surveys, we achieve >90 per cent tighter constraints on S₈, but also on the Hubble and dark energy equation-of-state parameters. Interestingly, we find improvements when combining these two probes only in our Stage-III set-up; in the Stage-IV scenario the lensing PDFs contain all information from the standard two-point statistics and more. This suggests that while these two probes are currently complementary, the lower noise levels of upcoming surveys will unleash the constraining power of the PDF.