Computing the All-Orders Lensing Trispectrum of the CMB

Between the cosmic microwave background (CMB) surface of last scattering and our telescopes, large scale structure gravitationally deflects incoming photons, producing a lensing effect that alters the statistics of the observed sky. Lensing introduces non-stationary CMB statistics and (on average) a non-vanishing connected trispectrum component, which is essential for a complete description of CMB statistics. Computing the lensing trispectrum allows for the extraction of a wealth of CMB information, including the total signal-to-noise of lensing effects in the CMB, the amount of information recovered from lensing estimators, and the lensing-induced non-Gaussian power spectrum covariance. We discuss our recent advances in the analytic and numerical computation of the all-orders lensing trispectrum for both flat-sky and full-sky regimes, and the information gain brought forth by said calculations.