Searching for inflationary physics with the CMB trispectrum. I. Primordial theory and optimal estimators
Phys. Rev. D 111, 123532 – Published 17 June, 2025
DOI: https://doi.org/10.1103/wkj2-q62t
Abstract
The primordial four-point function encodes a wealth of information about the inflationary Universe. Despite extensive theoretical work, most models of four-point physics have never been compared to data. In this series, we conduct a detailed analysis of cosmic microwave background temperature and polarization trispectra, searching for a wide variety of phenomena including local effects, self-interactions, curvatons, Dirac-Born-Infeld inflation, gauge fields, solid inflation, scalar field exchange, spinning massive field exchange, chiral physics, point sources, and gravitational lensing. After presenting a suite of separable primordial templates, we derive 13 quasioptimal estimators that directly estimate the underlying template amplitudes. These are unbiased, minimum variance, mask deconvolved, and account for correlations between templates (including with lensing). Each estimator can be efficiently implemented using spherical harmonic transforms, Monte Carlo methods, and optimization techniques, and asymptotes to standard forms in certain limits. In Paper II [O. H. E. Philcox, Phys. Rev. D 111, 123533 (2025)], we implement these estimators in public code, and in Paper III [O. H. E. Philcox, Phys. Rev. D 111, 123534 (2025)], use them to constrain primordial trispectra with Planck data. This enables a wide variety of tests of inflation, including some of the first direct constraints on cosmological collider physics.
