New Fast Algorithm for Computing Bispectrum Multipoles in Cosmological Data
Researchers have developed a fast, FFT-based estimator that computes all angular multipole moments of the redshift-space bispectrum with a computational complexity of O(N_g^4), compared to O(N_g^6) for direct methods. The bispectrum encodes non-Gaussian cosmological information through the orientational dependence of triangle configurations formed by three Fourier modes relative to the line of sight. The improvement in efficiency could significantly expand the cosmological information extractable from galaxy redshift surveys and future 21-cm observations.
A new estimator published in Physical Review D offers a computationally efficient method for calculating the angular multipole moments B_ℓ^m of the redshift-space bispectrum, a three-point statistical measure of large-scale structure. By leveraging Fast Fourier Transforms, the algorithm reduces the scaling of computation time from O(N_g^6) to O(N_g^4) for a gridded data cube of volume N_g^3, representing a substantial practical speedup for realistic survey volumes. Crucially, the estimator handles all values of ℓ and m, including the previously underutilized m≠0 multipoles, which carry additional cosmological information beyond the standard m=0 case. The method was validated against a simulated non-Gaussian field with known analytical bispectrum multipoles, finding good agreement across all 16 non-zero multipoles up to ℓ=6, m=6. The authors anticipate that incorporating m≠0 multipoles will meaningfully enhance parameter constraints from upcoming galaxy surveys and redshifted 21-cm cosmology experiments.
What's missing
The paper does not quantify the expected improvement in cosmological parameter constraints (e.g., on primordial non-Gaussianity or growth rate) from including m≠0 multipoles, nor does it discuss the practical memory or I/O overhead introduced by the FFT-based approach at survey-scale grid sizes. The validation is performed on a simulated non-Gaussian field rather than on realistic mock galaxy catalogs that include survey geometry, selection effects, or noise, leaving open questions about performance in observational settings.
What different sources said
- arXiv astro-phCenter
Brisk estimator for the angular multipoles of the redshift space bispectrum
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