Bye binormal: analysing the joint PDF of galaxy density and weak lensing convergence

Abstract: At any given scale, 3$\times$2-point statistics extract only three numbers from the joint distribution of the cosmic matter density and galaxy density fluctuations: their variances and their covariance. It is well known that the full shape of the PDF of those fluctuations contains significantly more information than can be accessed through these three numbers. But the study of the PDF of cosmic density fluctuations in real observational data is still in its infancy. Here we present \verb|CosMomentum|, a public software toolkit for calculating theoretical predictions for the full shape of the joint distribution of a line-of-sight projected tracer density and the gravitational lensing convergence. We demonstrate that an analysis of this full shape of the PDF can indeed disentangle complicated tracer bias and stochasticity relations from signatures of cosmic structure growth. Our paper also provides back-drop for an upcoming follow-up study, which prepares PDF analyses for application to observational data by incorporating the impact of realistic weak lensing systematics.