A fast estimator for quantifying the shape dependence of the 3D bispectrum

Abstract

The dependence of the bispectrum on the size and shape of the triangle contains a wealth of cosmological information. Here we consider a triangle parameterization which allows us to separate the size and shape dependence. We have implemented an FFT based fast estimator for the three dimensional (3D) bin averaged bispectrum, and we demonstrate that it allows us to study the variation of the bispectrum across triangles of all possible shapes (and also sizes). The computational requirement is shown to scale as $\sim N_{\mathrm{g}}^3\log N_{\mathrm{g}}^3$ where $N_g$ is the number of grid points along each side of the volume. We have validated the estimator using a non-Gaussian field for which the bispectrum can be analytically calculated. The estimated bispectrum values are found to be in good agreement ($<10\%$ deviation) with the analytical predictions across much of the triangle-shape parameter space. We also introduce linear redshift space distortion, a situation where also the bispectrum can be analytically calculated. Here the estimated bispectrum is found to be in close agreement with the analytical prediction for the monopole of the redshift space bispectrum.

21 pages, 11 figures, Accepted for publication in JCAP

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• The size and shape dependence of the SDSS galaxy bispectrum
• Redshift-space galaxy bispectrum in presence of massive neutrinos: A multipole expansion approach for Euclid
• The Effect of Large Optical Depths on the Non-Gaussian 21-cm signal from Cosmic Dawn
• Probing the large-scale structure with 21cm-galaxy cross-bispectrum: Estimates from simulations and forecasts for upcoming cosmological surveys