One Loop Galaxy Bispectrum

Computation of the one-loop bispectrum of galaxies in redshift space, using Mathematica. This is described in Philcox+22.

NOTE: This code is now depracated. It has been replaced by new code derived for https://arxiv.org/abs/2507.22110, which implements the COBRA factorization scheme and fixes a number of bugs. Please contact Oliver if you're interested in using the new code.

The code contains a number of components:

1. Kernels.nb & KernelsFlat.nb: Computation and simplification of the bispectrum kernels using Mathematica [cosmology-independent]. These are saved in the kernels directory.
2. Spectra.wls & SpectraFlat.wls: Computation of the full and flattened bispectrum templates, given the pre-computed integration kernels. These scripts compute the templates for all bias parameters and a single angular component. They are designed to be run on a HPC cluster using Mathematica. We provide a sample SLURM submission script for computing all templates.
3. Output.wls: Read-in and combination of the bispectrum templates using Mathematica. These are saved as two HDF5 files.
4. Bispectrum Interpolation.ipynb: Interpolation and extraction of the one-loop bispectrum using Python. This demonstrates the practical usage of the one-loop bispectrum, including full radial and angular bin-integration, and Alcock-Paczynski distortions. Steps 1-3 are performed for both flattened (k1 = k2 + k3) and full bispectrum shapes, to allow for efficient and numerically stable interpolation. Note that step 1 only needs to be run if the bispectrum kernels themselves are being modified, else the default kernels provided can be used.

A necessary input to stage (2) is the IR-resummed power spectrum in the pk directory; this can be computed using CLASS-PT, and we provide a sample spectrum. High-resolution bispectrum templates (the output of step 3) computed using the PT Challenge best-fit power spectrum can be downloaded from Google Drive, and are those used in the Philcox+22 paper.

The computed spectra can be interfaced with the power spectrum and bispectrum likelihoods found here.

Authors

• Oliver Philcox (Princeton / IAS)
• Mikhail Ivanov (IAS)
• Marko Simonovic (CERN)