Probing Cosmology through Higher-Order CMB Lensing Statistics

Abstract

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 $Ω_m$, the scalar power spectrum amplitude $A_s$, and the neutrino mass sum $M_ν$. 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 $Ω_m$ and $A_s$, respectively, and a 70% reduction in the one-sided uncertainty on $M_ν$. 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 $σ(M_ν)$ and 35% in $σ(Ω_m)$ 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.

Figures (21)

• Figure 1: The 101 sampled cosmologies from the MassiveNuS suite. Each panel shows a 2D projection of the sampled parameter space, illustrating the distribution of $(M_\nu, \Omega_m, 10^9 A_s)$ across the simulation set.
• Figure 2: Lensed CMB temperature (TT) and polarization (EE/BB) signal and noise power spectra for the expected nominal SO observations SimonsObservatory:2018koc after component separation.
• Figure 3: Fiducial $C_\ell^{\kappa\kappa}$ (orange) and the lensing reconstruction noise $N^{(0)}$ (blue) estimated from the minimum variance combination expected for an SO-nominal-like experiment. The green line indicates the mean and standard deviation of $C_{\ell^{\kappa\kappa}}$ from 10,000 realizations of MassiveNuS at the fiducial cosmology. We can see that the differences between CAMB and MassiveNuS begin to increase beyond $\ell\sim2000$ due to the finite resolution of the simulation.
• Figure 4: Lensing reconstruction performance for a single MassiveNuS convergence map, averaged over 1,000 different realizations of unlensed CMB maps using the minimum variance quadratic estimator. The reconstructed $\kappa$ power spectrum (orange) and the noise bias $N^{(0)}$ (purple) are shown along with their difference (green) compared to the true input spectrum (blue). The cross-spectrum between the reconstructed and true $\kappa$ fields (dotted red) demonstrates excellent consistency, validating the reconstruction pipeline.
• Figure 5: True ($\phi_{\rm true}$) and reconstructed ($\phi_{\rm recon}$) CMB lensing potential maps from one MassiveNuS realization, shown at the map-level, together with their difference ($\phi_{\rm recon}-\phi_{\rm true}$). The reconstructed map recovers the main structures of the true potential, demonstrating the performance of our lensing reconstruction pipeline. Note that we apply a simple top-hat filter in Fourier space for both fields with $\ell_{\rm min}=200$ and $\ell_{\rm max}=4000$ here; thus, some small-scale noise clearly remains in the reconstructed map. Also, note that the small-scale smoothness of $\phi_{\rm true}$ is due to the resolution of the simulation, as shown in Figure \ref{['fig:kappa_cl']}.