Unleashing Cosmic Shear Information with the Tomographic Weak Lensing PDF

In this work, we demonstrate the constraining power of the tomographic weaklensing convergence PDF for StageIV-like source galaxy redshift bins and shapenoise. We focus on scales of 10 to 20 arcmin in the mildly nonlinearregime, where the convergence PDF and its changes with cosmological parameterscan be predicted theoretically. We model the impact of reconstructing theconvergence from the shear field using the well-known Kaiser-Squires formalism.We cross-validate the predicted and the measured convergence PDF derived fromconvergence maps reconstructed using simulated shear catalogues. Employing aFisher forecast, we determine the constraining power for(Ω_m,S_8,w_0). We find that adding a 5-bin tomography improves theκ-PDF constraints by a factor of {3.8,1.3,1.6} for (Ω_m,S_8,w_0) respectively. Additionally, we perform a joint analysis with theshear two-point correlation functions, finding an enhancement of around afactor of 1.5 on all parameters with respect to the two-point statisticsalone. These improved constraints come from disentangling Ω_ m fromw_0 by extracting non-Gaussian information, in particular, including the PDFskewness at different redshift bins. We also study the effect of varying thenumber of parameters to forecast, in particular we add h, finding that theconvergence PDF maintains its constraining power while the precision fromtwo-point correlations degrades by a factor of {1.7,1.4,1.8} for{Ω_ m,S_8,w_0}, respectively.