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Optimal Estimation of the Binned Mask-Free Power Spectrum, Bispectrum, and Trispectrum on the Full Sky: Tensor Edition
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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 Philcox (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 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 phenomena, such as non-separable inflationary physics (novelly including polarized trispectra), non-linear evolution in the late Universe, and cosmic parity-violation.
Forward citations
Cited by 4 Pith papers
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Dissecting the Scalar Cosmological Collider with the Cosmic Microwave Background
A joint Bayesian fit of the multi-field inflationary Lagrangian to Planck bispectrum data finds no cosmological collider signal (max Δχ²=5.3) and shows weak-mixing template searches are invalid except at the smallest masses.
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Searching for Inflationary Physics with the CMB Trispectrum: 2. Code & Validation
PolySpec is a public, validated suite of near-optimal quartic estimators that lets the CMB four-point function probe many inflationary models beyond local non-Gaussianity.
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Searching for Inflationary Physics with the CMB Trispectrum: 1. Primordial Theory & Optimal Estimators
A set of quasi-optimal CMB trispectrum estimators is derived for local, EFT, direction-dependent, spinning-particle, point-source, and lensing templates, enabling first collider searches.
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Searching for Inflationary Physics with the CMB Trispectrum: 3. Constraints from Planck
A comprehensive Planck PR4 trispectrum analysis finds no primordial non-Gaussianity across 33 templates and sets leading constraints, including tau_NL loc < 1500 at 95% CL.
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