Optimal estimation of the binned mask-free power spectrum, bispectrum, and trispectrum on the full sky: Tensor edition
Oliver H. E. Philcox
Abstract
We derive optimal estimators for the binned two-, three-, and four-point correlators of statistically isotropic tensor fields defined on the sphere, in the presence of arbitrary beams, inpainting, and masking. This is a conceptually straightforward extension of the associated scalar-field estimators [O. H. E. Philcox, Phys. Rev. D 107, 123516 (2023).], but upgraded to include spin-2 fields such as cosmic microwave background polarization and galaxy shear, and parity-violating physics in all correlators. All estimators can be realized using spin-weighted spherical harmonic transforms and Monte Carlo summation and are implemented in the public code polybin, with computation scaling, at most, with the total number of bins. We perform a suite of validation tests verifying that the estimators are unbiased and, in limiting regimes, minimum variance. These facilitate general binned analyses of higher-point functions, and allow constraints to be placed on various pheomena, such as nonseparable inflationary physics (novelly including polarized trispectra), nonlinear evolution in the late Universe, and cosmic parity violation.