Efficient computation of the galaxy angular bispectrum in redshift space
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914614575366144 |
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| author | Gao, Zucheng Vlah, Zvonimir Challinor, Anthony |
| author_facet | Gao, Zucheng Vlah, Zvonimir Challinor, Anthony |
| contents | Efficient computation of the angular bispectrum is an essential part of modelling large-scale structure observations, but it still remains an extremely challenging task. In this work, we compute the tree-level, unequal-time angular bispectrum in both real and redshift space. By deriving full-sky results, we show that the bispectrum can be expressed as a sum of products of two angular power spectra, enabling the use of our recently developed flat-sky approximation to enhance computational efficiency significantly. This flat-sky formalism preserves key line-of-sight mode information while discarding extraneous full-sky contributions. We validate our approach by comparing it with direct full-sky integration, finding excellent agreement across a wide range of scales and redshifts for all bispectrum configurations. At redshift $z = 1$, we achieve sub-percent agreement (for multipoles $\ell \gtrsim 5$) between full-sky and flat-sky results for equilateral, squeezed, and folded configurations, using narrow Gaussian radial window functions ($σ_z = 0.01$) in both equal-time and unequal-time scenarios. On small scales, where direct full-sky integration becomes computationally prohibitive, our results align with the Limber approximation (where applicable), confirming the robustness and accuracy of our implementation. To facilitate future studies, we provide a \texttt{Python} implementation of our results, which is publicly available on \texttt{GitHub}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_30246 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient computation of the galaxy angular bispectrum in redshift space Gao, Zucheng Vlah, Zvonimir Challinor, Anthony Cosmology and Nongalactic Astrophysics Efficient computation of the angular bispectrum is an essential part of modelling large-scale structure observations, but it still remains an extremely challenging task. In this work, we compute the tree-level, unequal-time angular bispectrum in both real and redshift space. By deriving full-sky results, we show that the bispectrum can be expressed as a sum of products of two angular power spectra, enabling the use of our recently developed flat-sky approximation to enhance computational efficiency significantly. This flat-sky formalism preserves key line-of-sight mode information while discarding extraneous full-sky contributions. We validate our approach by comparing it with direct full-sky integration, finding excellent agreement across a wide range of scales and redshifts for all bispectrum configurations. At redshift $z = 1$, we achieve sub-percent agreement (for multipoles $\ell \gtrsim 5$) between full-sky and flat-sky results for equilateral, squeezed, and folded configurations, using narrow Gaussian radial window functions ($σ_z = 0.01$) in both equal-time and unequal-time scenarios. On small scales, where direct full-sky integration becomes computationally prohibitive, our results align with the Limber approximation (where applicable), confirming the robustness and accuracy of our implementation. To facilitate future studies, we provide a \texttt{Python} implementation of our results, which is publicly available on \texttt{GitHub}. |
| title | Efficient computation of the galaxy angular bispectrum in redshift space |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2605.30246 |