🌀 ang_bispec: Python code for galaxy number count angular bispectrum

Based on T. Montandon, et al., “Angular bispectrum of matter number counts in cosmic structures,” arXiv:2501.05422 (2025).

Description
ang_bispec is a high-performance Python implementation for computing the angular bispectrum of galaxy number counts. It significantly extends the existing Byspectrum code by incorporating finite redshift bins, redshift-space distortions (RSD), and leading general relativistic (GR) projection and radiation effects, all without relying on the Limber approximation.

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Features

• Complete theoretical model
  Based on first- and second-order number count expressions from the literature, covering:

  • Newtonian terms (density, RSD, quadratic terms)
  • Non‑integrated projection effects
  • Radiative and dynamical GR effects

• Efficient hypergeometric evaluation
  Translated the Mathematica expressions from Assassi et al. (2017) into numba‑accelerated Python for fast computation of the ₂F₁ hypergeometric function.

• Pipeline overview

  1. Linear cosmology module
     • Solves growth functions D(z), f(z), v(z), w(z)
     • Interfaces with CLASS to extract potential transfer functions and power spectra
  2. FFTLog module
     • Computes Hankel transforms of the potential power spectrum and transfer function
  3. Generalized power spectra (C_ℓ(χ))
     • Precomputes 7 spectra across ℓ and χ values—this is the main bottleneck
  4. Precomputation of radial integrals
     • Integrals over (r_1) for all (f_{n,m}) coefficients
  5. Main bispectrum loop
     • Computes contributions for all (ℓ₁, ℓ₂, ℓ₃) triplets, including:
       • Density, RSD, projection, quadratic, and cross terms

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Prerequisites

• Python ≥3.8
• numba for JIT acceleration
• CLASS installed and accessible

Installation

Clone the repo and install dependencies:

git clone https://github.com/TomaMTD/ang_bispec.git
cd ang_bispec