Analytical integration of EFTofLSS loop corrections

This project was created to efficiently evaluate ETFofLSS loop corrections up to the 1-loop bispectrum. This technique uses a decomposition of the linear power spectrum into analytical function of $k^2$, and proceeds to evaluate the integrals using recursion relations. The algorithm is described in detail in arXiv:2212.07421.

Outline

• 1. source/: where all the computation scripts are.
• 3. Ctabs/: the exponent tables and the $k$'s and/or triangles to evaluate are here.
• integer_powers.nb: Mathematica notebook with the calculation of $P_{22}$ and $B_{222}$ with our method and a comparison with numerical integration.

Installation

The main script is 1. source/babiscython_v4_ubuntu.pyx and is written in Cython. It calculates the function $L$. To compile it, one needs to run 1. source/setup_babiscython_ubuntu.py the following way:

python setup_babiscython_ubuntu.py build_ext --inplace

After this, one needs to compile the script 1. source/Jfunc_cython_v4.pyx which calculates the $J$ function from the $L$ function. To compile it, one needs to run

python setup_jfunc.py build_ext --inplace

The file 1. source/config.py contains the cache for memoization of the $L$-function.

Example of usage

The remaining files calculate individual loops. For example, running

python B222_bias.py

Calculates the bias-decomposed $J$-function for a given set of triangles.

The notebook 1. source/Test and run functions.ipynb provides other examples of usage. The Mathematica notebook integer_powers.nb contains the full pipeline to calculate $P_{22}$ and $B_{222}$.