The Needlet CMB Trispesctrum

TL;DR

This paper introduces a computationally efficient estimator for the needlet trispectrum in CMB data, leveraging needlet localization to handle masked regions and including corrections for noise and sky cuts, aiding in nonlinearity parameter estimation.

Contribution

It presents a novel, feasible estimator for the needlet trispectrum that improves on previous methods by exploiting needlet localization and incorporating noise corrections.

Findings

Estimator handles masked regions effectively

Includes quadratic correction for noise and sky cuts

Provides analytic statistical properties for guidance

Abstract

We propose a computationally feasible estimator for the needlet trispectrum, which develops earlier work on the bispectrum by Donzelli et al. (2012). Our proposal seems to enjoy a number of useful properties, in particular a) the construction exploits the localization properties of the needlet system, and hence it automatically handles masked regions; b) the procedure incorporates a quadratic correction term to correct for the presence of instrumental noise and sky-cuts; c) it is possible to provide analytic results on its statistical properties, which can serve as a guidance for simulations. The needlet trispectrum we present here provides the natural building blocks for the efficient estimation of nonlinearity parameters on CMB data, and in particular for the third order constants $g_{NL}$ and $\tau_{NL}$.