Probing cosmology through higher-order CMB lensing statistics

We investigate the cosmological information in higher-order statistics of the cosmic microwave background (CMB) lensing convergence field for a near-term experiment with noise properties similar to the Simons Observatory (SO). Using a fully field-level forward-modeling pipeline based on ray-traced simulations from the massivenus suite and realistic SO-like CMB lensing reconstruction, we naturally include nonlinear structure formation, post-Born effects, and higher-order reconstruction noise. We measure several non-Gaussian statistics, including Minkowski functionals, peak and minima counts, moments, and wavelet-scattering coefficients. We train Gaussian-process emulators to model each statistic’s dependence on the matter density fraction Ω𝑚, the scalar power spectrum amplitude 𝐴𝑠, and the neutrino mass sum 𝑀𝜈. We quantify the relative information gain these statistics provide beyond the lensing power spectrum and identify which are most robust to reconstruction noise. We find that morphology-based statistics, particularly Minkowski functionals and peak/minima counts, offer significant complementary constraining power: combining all non-Gaussian statistics with the power spectrum yields reductions of 40% and 38% in the marginalized uncertainties on Ω𝑚 and 𝐴𝑠, respectively, and a 70% reduction in the one-sided uncertainty on 𝑀𝜈. These gains remain non-negligible even when the power spectrum is extended to larger scales and combined with primary CMB and BAO data, with Minkowski functionals providing an additional 11% improvement in 𝜎⁡(𝑀𝜈) and 35% in 𝜎⁡(Ω𝑚) beyond the extended power spectrum. By contrast, moments and wavelet-scattering coefficients provide more limited gains at SO noise levels. Our results highlight the potential of non-Gaussian statistics to enhance cosmological constraints from SO and future CMB surveys.