Brisk estimator for the angular multipoles of the redshift space bispectrum

Abstract

The anisotropy of the redshift space bispectrum depends upon the orientation of the triangles formed by three $\mathbf{k}$ modes with respect to the line of sight. For a triangle of fixed size ($k_1$) and shape ($\mu ,t$), this orientation dependence can be quantified in terms of angular multipoles $B_{\ell }^m(k_1,\mu ,t)$ which contain a wealth of cosmological information. We propose a fast and efficient FFT-based estimator that computes the bispectrum multipole moments $B_{\ell }^m$ of a 3D cosmological field for all possible $\ell$ and $m$ (including $m\ne 0$). The time required by the estimator to compute all multipoles from a gridded data cube of volume $N_g^3$ scales as $\sim \mathcal{O}(N_g^4)$ in contrast to the direct computation technique which requires time $\sim \mathcal{O}(N_g^6)$. Here, we demonstrate the formalism and validate the estimator using a simulated non-Gaussian field for which the analytical expressions for all the bispectrum multipoles are known. The estimated results are found to be in good agreement with the analytical predictions for all $16$ non-zero multipoles (up to $\ell =6,m=6$). We expect the $m\ne 0$ bispectrum multipoles to significantly enhance the information available from galaxy redshift surveys and future redshifted 21-cm observations.

12 pages, 6 figures; Published in PRD

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Cited by in corpus (1)

• Probing gravity beyond general relativity with bispectrum multipoles of cosmological tracers: I. Theoretical Foundations