Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background II: Partial Sky Coverage and Inhomogeneous Noise

TL;DR

This paper introduces a computationally efficient estimator for primordial non-Gaussianity in the CMB, capable of handling partial sky coverage and inhomogeneous noise, enabling optimal analysis of upcoming high-sensitivity data.

Contribution

It generalizes a previous bispectrum estimator to realistic observational conditions while maintaining computational efficiency, scaling as O(N^{3/2}).

Findings

Efficient estimator scales as O(N^{3/2})

Handles partial sky coverage and inhomogeneous noise

Prepares for analysis of future high-sensitivity CMB data

Abstract

In our recent paper (Yadav et al. 2007) we described a fast cubic (bispectrum) estimator of the amplitude of primordial non-Gaussianity of local type, f_{NL}, from a combined analysis of the Cosmic Microwave Background (CMB) temperature and E-polarization observations. In this paper we generalize the estimator to deal with a partial sky coverage as well as inhomogeneous noise. Our generalized estimator is still computationally efficient, scaling as O(N^3/2) compared to the O(N^5/2) scaling of the brute force bispectrum calculation for sky maps with N pixels. Upcoming CMB experiments are expected to yield high-sensitivity temperature and E-polarization data. Our generalized estimator will allow us to optimally utilize the combined CMB temperature and E-polarization information from these realistic experiments, and to constrain primordial non-Gaussianity.