cosmostat

Python library to estimate chi-square constraints on cosmology models using background quantities.

Installation 🧱

Cosmostat project uses poetry as the package and dependency manager. If poetry is not installed in your system, you can follow the installation instructions at the poetry website.

To install cosmostat, it is recommended to create a virtual environment isolated from the main Python interpreter. We have several tools to create a virtual environment, being conda the recommended tool for handling virtual environments and software packages (for now).

Using conda to manage virtual environments

The following sections assume we have conda already installed on our computers. The recommended way to obtain conda is by installing Miniconda, which is available for Linux, Mac OS, and Windows. Please refer to the conda user guide for installation, help, and usage instructions.

Creating a virtual environment

Since poetry handles cosmostat dependencies, we only need conda to create a minimum, isolated virtual environment. Cosmostat requires Python 3.7 and above to properly work, so we can create the virtual environment as follows:

conda create -n cosmostatenv python=3.7

This environment contains python 3.7 as the interpreter and a few packages. Once created, we only must activate it,

conda activate cosmostatenv

Installing cosmostat in development mode

Once the virtual environment has been activated, type the following instruction at the cosmostat root directory:

poetry install

This command will install cosmostat and all of its dependencies in the cosmostatenv virtual environment. We can have a look at all the installed packages in the environment by calling conda list. For most packages, conda will indicate they were installed from PyPI, since they were installed by poetry, not by conda.

In addition to installing cosmostat dependencies, poetry will install the cosmostat package (located in the src subdirectory) in development mode. Therefore, the cosmostat package will be importable from any python script or jupyter notebook as a regular python package.

Workaround for macOS M1-Powered Machines

By May 2022, installing the dependencies on a macOS computer powered by the M1 processors may not be possible at first. This issue arises from the lack of ARM64 compiled packages for some dependencies: Pillow, and llvmlite, in PyPI. On the other hand, the above problem does not occur if we use conda to install the project dependencies from the conda-forge channel. However, if we use conda, we still face a challenge: how to install cosmostat in development mode?, since this process depends on executing the poetry install command (we will explain this problem with more detail some lines below).

We propose the following workaround to install cosmostat dependencies and enable it in development mode.

1. Install the project dependencies in a new conda environment using the conda env create command with an environment definition file. This project has its own files, conda/env-specs/default.yml for Linux and macOS, and conda/env-specs/default-win.yml for Windows, with the dependency list, including both mandatory and development packages. We can create the new environment and install every dependency with the following command:

   conda env create -f conda/env-specs/default.yml

   After executing the above command, we should have a new conda environment named cosmostatenv, with everything needed to start developing.

2. Remove the complete list of dependencies in the pyproject.toml file. More specifically, delete all the dependencies under tool.poetry.dependencies and tool.poetry.dev-dependencies, except for Python.

3. Execute poetry install. This command will install cosmostat in development mode, but it will not install any other dependency.

This workaround is needed because poetry will try to install the project dependencies as specified in the poetry.lock file, so it may remove any packages previously installed by conda to match the lock file contents. After we remove any packages in the pyproject.toml file (except for Python), poetry will not touch any of the packages previously installed by conda. NOTE: this method will install Python 3.8 as the interpreter.

The above procedure has a significant drawback: it makes the development process non-reproducible. The reason for this is that conda lacks a mechanism to lock package versions, that is, to generate a lock file with a similar purpose to the poetry.lock file. Then, every time we create a new environment using conda env create -f, the package versions may change among different executions.

Command Line Interface

After installing in development mode, we can use the CLI of the library, whose functionality is contained in the cosmostat (cosmostat.exe on Windows) executable.

We can access the command help pages through

cosmostat --help

Information about the models and datasets

We can get information about the implemented models and observational datasets with the info subcommand,

cosmostat info

For example, the CPL model accepts the following parameters,

  Name            Parameters
         ┏━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
  CPL    ┃    Name     ┃  Default   ┃
         ┃             ┃   Value    ┃
         ┡━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
         │     w0      │    ---     │
         │     w1      │    ---     │
         │      h      │   0.6731   │
         │  omegabh2   │  0.02222   │
         │  omegach2   │   0.1197   │
         └─────────────┴────────────┘

$\chi^2$-fitting and optimization procedure

By using the CLI, we can fit a cosmological model to one or more observational datasets. We do this by minimizing the $\chi^2$ as a function of the model parameters. This procedure is realized through the chi-square-fit subcommand,

cosmostat chi-square-fit

This command takes two arguments: the EOS_MODEL, and the DATASET (or a union of one or more datasets). We must then specify the optimization parameters bounds, or fix one or more of them with the --param option. We also must supply an output file to save the best-fit parameters through the -o option.

For example, we could try to fit the CPL model to the BAO dataset. According to the model information, the CPL model requires specifying, at least, the parameters w0 and w1. The rest of the parameters are optional; if omitted, the routine assumes they take their default values. We can define the fitting procedure as follows:

• We want w0 to lie in the interval [-3, 1]. We pass the option --param w0 -3:1.
• We want w1 to lie in the interval [0, 1]. We pass the option --param w1 -0:1.
• We have to fix h to 0.5. We use --param h 0.5.
• Parameters omegabh2 and omegach2 keep their default values. We can omit them from the command.
• The best-fit result should be saved in a HDF5 file named ./best-fit-cpl#1.h5 in the current working directory. We pass the option -o ./best-fit-cpl#1.h5.

In summary, the full command line for this fitting becomes

cosmostat chi-square-fit CPL BAO --param w0 -3:1 --param w1 0:1 --param h 0.5 -o ./best-fit-cpl#1.h5

The program shows the execution progress and the best-fit result.

We can always see the detailed chi-square-fit subcommand usage through the --help option.

Evaluation of $\chi^2$ in a parameter grid

In addition to fitting, we can evaluate the $\chi^2$ on a parameter grid. We do this through the chi-square-grid subcommand,

cosmostat chi-square-grid

Its usage is similar to the chi-square-fit command: we pass a model and a dataset as arguments. We also specify the parameters that define the grid and/or parameters that should be held fixed. For non-fixed parameters, we have to indicate a partition to evaluate $\chi^2$, i.e., the partition bounds and how many elements it should have.

For example, we could evaluate the $\chi^2$ of the CPL model, together with the BAO dataset. We can define the procedure as follows:

• We want a partition over w0 in the interval [-3, 1] with 100 items. We pass the option --param w0 -3:1:100.
• We want a partition over w1 in the interval [0, 1] with 100 elements. We use the option --param w1 -0:1:100.
• Parameters h, omegach2, and omegabh2 keep their default values. We can omit them from the command.
• The best-fit result should be saved in an HDF5 file named ./grid-cpl-bao#1.h5 in the current working directory. We pass the option -o ./grid-cpl-bao#1.h5.

The full command line to evaluate the grid becomes

cosmostat chi-square-grid CPL BAO --param w0 -3:1:100 --param w1 0:1:100 -o ./grid-cpl-bao#1.h5

The program shows the grid evaluation progress. By default, it uses all of the system's available processes for evaluating the $\chi^2$ in parallel.

Developing the code

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

https://github.com/MarianaJBr/cosmostat/

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.

Using the code

You can use this software freely, provided that in your publications, you cite at least the paper " A single parameterization for dark energy and modified gravity models" http://arxiv.org/abs/2102.08561 but feel free to also cite " Modified gravity for surveys" https://arxiv.org/abs/1804.04284 and "Probing a Steep EoS for Dark Energy with latest observations" https://arxiv.org/abs/1708.08529

Authors

• Mariana Jaber, https://github.com/MarianaJBr, INSPIRE Profile
• Luisa Jaime, https://github.com/luisajaime, INSPIRE Profile
• Gustavo Arciniega, https://github.com/gustavoarciniega , INSPIRE Profile
• Omar Abel Rodríguez-López , https://github.com/oarodriguez/