Skewing the CMB×LSS: a fast method for bispectrum analysis

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.

Analysis of BOSS galaxy data with weighted skew-spectra

“…With these comparisons, we can see that even though the skew-spectrum serves as a compression of the full bispectrum, the error bars we present are competitive with the full bispectrum analysis. This was also noted in our previous work [28] with harmonic-space skew-spectra in which we have shown, through a Fisher forecast, that skew-spectra with Legendre polynomial kernels are sufficient to constrain not only the bias parameters, but also the seven νΛCDM parameters. In this work, we include two additional kernels to capture shapes from primordial non-Gaussianity.…”

“…Refs. [20,22,23] studied such skew-spectra for the galaxy bispectrum in Fourier space, and these were subsequently extended to redshift-space bispectra [24][25][26] and harmonic space for weak-lensing analyses [27,28]. In this paper, we present the first application of skew-spectra to LSS data.…”

“…In order to obtain the theory skew-spectrum, we must specify the kernels used, S(k, k ′ ). From our previous work [28], we know that Legendre polynomial kernels can preserve much of the information from the full bispectrum analysis. The result from Fisher analysis shows that there is only at most 12% difference on the error of bias parameters compared with the full bispectrum analysis, even when we marginalize over ΛCDM parameters.…”

Cosmological information in skew spectra of biased tracers in redshift space

“…Among the proposed statistics, the weighted galaxy skew spectra [34,[40][41][42][43] are simple and computationally efficient proxy statistics for the galaxy bispectrum, constructed from the cross-correlation of the observed galaxy density field with an appropriately weighted square of it. 7 Since the forms of the skew spectra are derived from the maximum likelihood estimator of the amplitude of the bispectrum [34], in the limit of weak non-Gaussianity, they carry the same Fisher information as the full bispectrum for parameters that appear as overall amplitudes of the separable contributions of tree-level bispectrum.…”

“…Third, estimating the covariance matrices of the skew spectra from mocks requires a significantly smaller number of mocks 6 See [6][7][8][9] for recent works on galaxy 4-point statistics, [10][11][12] for statistics beyond n-point correlation functions using wavelets, and [13][14][15][16][17] for summary statistics capturing the environmental dependence of clustering. 7 Optimally weighted skew spectra in harmonic space, which saturate the Cramer-Rao bound of the bispectrum in the weakly non-Gaussian limit, were first introduced in the context of constraining primordial non-Gaussianity from the CMB data [44,45] (see [43,46,47] for some recent works on the harmonic-space skew and kurto spectra). 8 Analogous estimators for trispectrum, often referred to as kurto spectra, involve correlations of two quadratic fields or that of a cubic and linear field [47,48].…”