Skewing the CMB$\times$LSS: a Fast Method for Bispectrum Analysis

TL;DR

This paper introduces a fast, nearly-optimal skew-spectrum estimator for bispectrum analysis in cross-correlations of galaxy surveys and CMB lensing, providing comparable constraints with improved computational efficiency.

Contribution

It develops a new skew-spectrum method for bispectrum analysis that is faster and nearly as informative as traditional bispectrum approaches, validated with simulations.

Findings

Skew-spectrum constraints differ by at most 17% from bispectrum constraints.

The method can potentially achieve percent-level accuracy in bias parameter estimation.

Theoretical skew-spectra agree well with N-body simulation estimates.

Abstract

Upcoming cosmic microwave background (CMB) lensing measurements and tomographic galaxy surveys are expected to provide us with high-precision data sets in the coming years, thus paving the way for fruitful cross-correlation analyses. In this paper we study the information content of the weighted skew-spectrum, a nearly-optimal estimator of the angular bispectrum amplitude, as a means to extract non-Gaussian information on both bias and cosmological parameters from the bispectra of galaxies cross-correlated with CMB lensing, while gaining significantly on speed. Our results show that for the combination of the Planck satellite and the Dark Energy Spectroscopic Instrument (DESI), the difference in the constraints on bias and cosmological parameters from the skew-spectrum and the bispectrum is at most $17\%$. We further compare and find agreement between our theoretical skew-spectra and those estimated from N-body simulations, for which it is important to include gravitational non-linearities beyond perturbation theory and the post-Born effect for CMB lensing. We define an algorithm to apply the skew-spectrum estimator to the data and, as a preliminary step, we use the skew-spectra to constrain bias parameters and the amplitude of shot noise from the simulations through a Markov chain Monte Carlo likelihood analysis, finding that it may be possible to reach percent-level estimates for the linear bias parameter $b_1$.