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CLASS.VFDM: Cosmic Linear Anisotropy Solving System for an Ultralight Vector Field Dark Matter model

Authors: Tomás Ferreira Chase

In collaboration with M. Leizerovich, D. López Nacir, S. Landau.

Overview

This is a modification of CLASS v3.2.5 that replaces (or complements) the cold dark matter component with an ultralight Vector Field Dark Matter (VFDM) candidate: a massive, real, minimally-coupled Proca field. The code solves the full background evolution of the vector field and its linear perturbations (scalar and tensor sectors), and is able to produce CMB angular power spectra, the linear matter power spectrum, and the tensor (gravitational wave) sector sourced by the anisotropic stress of the vector field.

The physics, conventions and equations of motion follow the treatment presented in our companion paper:

  • T. Ferreira Chase, D. López Nacir - arxiv:2311.09373
  • T. Ferreira Chase, M. Leizerovich, D. López Nacir, S. Landau - arXiv:2408.12052
  • T. Ferreira Chase, D. López Nacir - arxiv:2604.21080

Please cite arXiv:2408.12052 (in addition to the standard CLASS references) if you use this code in a publication.

What is new with respect to standard CLASS

  • New background species vf (vector field) with its own energy density, pressure, shear and anisotropic stress, including the option of a homogeneous-but-anisotropic (Bianchi-I) background.
  • Modified scalar and tensor perturbation equations in a Bianchi-I background.
  • Gravitational wave sector sourced by the VFDM anisotropic stress.

Main VFDM input parameters

The new parameters are declared in the .ini file, together with the usual CLASS ones. The most relevant ones are:

  • Omega_vf : present-day density fraction of the vector field. Replaces (fully or partially) Omega_cdm. The budget equation is closed automatically by shooting.
  • vf_parameters : comma-separated list. The first entry is the vector field mass in eV (e.g. 1.e-22). The remaining entries are used by the shooting / initial-condition machinery. Example: vf_parameters = 1.e-22, 1.e-16, 1.e-30, 0.01.
  • vector_background_mode : frw or bianchi. Selects whether the background is assumed isotropic (FRW) or of Bianchi-I type, the latter being the physically consistent choice for a coherent vector field.
  • svt_coupling : yes / no. Switches on/off the scalar-vector-tensor coupling in the perturbation equations.
  • gamma_Ak : angle (in rad) between the background vector orientation and the Fourier mode k.

Python / notebooks

In notebooks/Python_wrapper/ we include the Jupyter notebooks used to produce the plots of the papers associated with this code, as well as further diagnostics.

Notebooks provided:

  • Background.ipynb — background evolution of the Proca field.
  • one_k.ipynb — scalar perturbations at a single k.
  • one_k_tensor.ipynb — tensor perturbations and GW sourcing.
  • one_k_gamma_sweep.ipynb — dependence of perturbations on gamma_Ak.
  • Pk_parametrization.ipynb, — matter power spectrum parameterization. Pk_theta_sweep.ipynb, — dependence of matter power spectrum on gamma_Ak. Pk_errors.ipynb — comparison of matter power spectrum with LCDM and a scalar field model.
  • Tensor_power_spectrum.ipynb — tensor power spectrum.
  • Velocity_invariant_transfer.ipynb — velocity-invariant transfer function.

The file class_env.yml lists the minimum requirements to create a conda environment for running CLASS.VFDM and the companion notebooks (tested on Ubuntu). Create it with conda env create -f class_env.yml and activate with conda activate class_env.

Below is the original CLASS documentation, which should be followed for instructions about installation and compilation of the code.

==============================================

CLASS: Cosmic Linear Anisotropy Solving System

Authors: Julien Lesgourgues, Thomas Tram, Nils Schoeneberg

with several major inputs from other people, especially Benjamin Audren, Simon Prunet, Jesus Torrado, Miguel Zumalacarregui, Francesco Montanari, Deanna Hooper, Samuel Brieden, Daniel Meinert, Matteo Lucca, etc.

For download and information, see http://class-code.net

Compiling CLASS and getting started

(the information below can also be found on the webpage, just below the download button)

Download the code from the webpage and unpack the archive (tar -zxvf class_vx.y.z.tar.gz), or clone it from https://github.com/lesgourg/class_public. Go to the class directory (cd class/ or class_public/ or class_vx.y.z/) and compile (make clean; make class). You can usually speed up compilation with the option -j: make -j class. If the first compilation attempt fails, you may need to open the Makefile and adapt the name of the compiler (default: gcc), of the optimization flag (default: -O4 -ffast-math) and of the OpenMP flag (default: -fopenmp; this flag is facultative, you are free to compile without OpenMP if you don't want parallel execution; note that you need the version 4.2 or higher of gcc to be able to compile with -fopenmp). Many more details on the CLASS compilation are given on the wiki page

https://github.com/lesgourg/class_public/wiki/Installation

(in particular, for compiling on Mac >= 10.9 despite of the clang incompatibility with OpenMP).

To check that the code runs, type:

./class explanatory.ini

The explanatory.ini file is THE reference input file, containing and explaining the use of all possible input parameters. We recommend to read it, to keep it unchanged (for future reference), and to create for your own purposes some shorter input files, containing only the input lines which are useful for you. Input files must have a *.ini extension. We provide an example of an input file containing a selection of the most used parameters, default.ini, that you may use as a starting point.

If you want to play with the precision/speed of the code, you can use one of the provided precision files (e.g. cl_permille.pre) or modify one of them, and run with two input files, for instance:

./class test.ini cl_permille.pre

The files *.pre are suppposed to specify the precision parameters for which you don't want to keep default values. If you find it more convenient, you can pass these precision parameter values in your *.ini file instead of an additional *.pre file.

The automatically-generated documentation is located in

doc/manual/html/index.html
doc/manual/CLASS_manual.pdf

On top of that, if you wish to modify the code, you will find lots of comments directly in the files.

Python

To use CLASS from python, or ipython notebooks, or from the Monte Python parameter extraction code, you need to compile not only the code, but also its python wrapper. This can be done by typing just 'make' instead of 'make class' (or for speeding up: 'make -j'). More details on the wrapper and its compilation are found on the wiki page

https://github.com/lesgourg/class_public/wiki

Plotting utility

Since version 2.3, the package includes an improved plotting script called CPU.py (Class Plotting Utility), written by Benjamin Audren and Jesus Torrado. It can plot the Cl's, the P(k) or any other CLASS output, for one or several models, as well as their ratio or percentage difference. The syntax and list of available options is obtained by typing 'pyhton CPU.py -h'. There is a similar script for MATLAB, written by Thomas Tram. To use it, once in MATLAB, type 'help plot_CLASS_output.m'

Developing the code

If you want to develop the code, we suggest that you download it from the github webpage

https://github.com/lesgourg/class_public

rather than from class-code.net. Then you will enjoy all the feature of git repositories. You can even develop your own branch and get it merged to the public distribution. For related instructions, check

https://github.com/lesgourg/class_public/wiki/Public-Contributing

Using the code

You can use CLASS freely, provided that in your publications, you cite at least the paper CLASS II: Approximation schemes <http://arxiv.org/abs/1104.2933>. Feel free to cite more CLASS papers!

Support

To get support, please open a new issue on the

https://github.com/lesgourg/class_public

webpage!