Galaxy bispectrum in the spherical Fourier-Bessel basis

Journal Article · Mon May 06 00:00:00 UTC 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.109.103507 · OSTI ID:2479620

Benabou, Joshua N.  ^[1]; Testa, Adriano  ^[2]; Heinrich, Chen  ^[2]; Gebhardt, Henry S. Grasshorn  ^[2]; Doré, Olivier  ^[2]

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1. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
2. California Institute of Technology (CalTech), Pasadena, CA (United States)

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z₂ into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

• Research Organization: California Institute of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: National Aeronautics and Space Administration (NASA); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0011632; SC0019225
• OSTI ID: 2479620
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 10 Vol. 109; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English