Searching for Inflationary Physics with the CMB Trispectrum: 1. Primordial Theory & Optimal Estimators

TL;DR

This paper develops optimal estimators for the CMB trispectrum to detect various inflationary physics signals, enabling detailed tests of inflation models using Planck data.

Contribution

It introduces a comprehensive set of separable primordial templates and quasi-optimal estimators for analyzing the CMB trispectrum, advancing the methodology for inflationary physics constraints.

Findings

Derived thirteen quasi-optimal estimators for primordial trispectra

Implemented estimators in public code for data analysis

Enabled constraints on inflation models using Planck data

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, DBI 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 thirteen quasi-optimal 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 2, we implement these estimators in public code, and in Paper 3, 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.