Symbolic Implementation of Extensions of the $\text{PyCosmo}$ Boltzmann Solver

Abstract

$\text{PyCosmo}$ is a Python-based framework for the fast computation of cosmological model predictions. One of its core features is the symbolic representation of the Einstein-Boltzmann system of equations. Efficient $\text{C/C++}$ code is generated from the $\text{SymPy}$ symbolic expressions making use of the $\text{sympy2c}$ package. This enables easy extensions of the equation system for the implementation of new cosmological models. We illustrate this with three extensions of the $\text{PyCosmo}$ Boltzmann solver to include a dark energy component with a constant equation of state, massive neutrinos and a radiation streaming approximation. We describe the $\text{PyCosmo}$ framework, highlighting new features, and the symbolic implementation of the new models. We compare the $\text{PyCosmo}$ predictions for the $\Lambda$CDM model extensions with $\text{CLASS}$, both in terms of accuracy and computational speed. We find a good agreement, to better than 0.1% when using high-precision settings and a comparable computational speed. Links to the Python Package Index (PyPI) page of the code release and to the PyCosmo Hub, an online platform where the package is installed, are available at: https://cosmology.ethz.ch/research/software-lab/PyCosmo.html.

35 pages including 5 figures and 3 tables. Link to $\text{PyCosmo}$ package: https://cosmology.ethz.ch/research/software-lab/PyCosmo.html

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• The NumPy array: a structure for efficient numerical computation
• Massive neutrinos and cosmology
• The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Dark energy with non-adiabatic sound speed: initial conditions and detectability
• Optimal Boltzmann hierarchies with non-vanishing spatial curvature

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