cosmoGW 0.0.26

code for cosmological gravitational wave backgrounds

CosmoGW v 1.0 (coming soon)

CosmoGW is a python library that can be installed using pip from the project stored in pypi

pip install cosmoGW

cosmoGW contains functions for the study of cosmological gravitational wave (GW) backgrounds from different sources in the early Universe, focusing on the production of GWs from sound waves and MHD turbulence from cosmological phase transitions.

It corresponds to an extension of the original GW_turbulence code previously used for calculations of GWs produced by MHD turbulence.

• Author: Alberto Roper Pol ([e-mail])
• Created: 01/12/2021 (GW_turbulence)
• Updated: 13/03/2025

The project includes state-of-the-art GW models developed by the community, postprocessing calculations, numerical computations, plotting routines, and detector sensitivities.

If you use any of the cosmoGW results, please cite this repository and the relevant reference/s listed in the routines, corresponding to the original published work.

I would also love to hear about your interest for this project and your work, so consider reaching out to me for any issues related to the code, questions or discussion: [e-mail].

Some of the routines use results from large-scale numerical simulations conducted with the open-source Pencil Code; see

[Pencil Code Collaboration], The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained, J. Open Source Softw. 6, 2807 (2021), arXiv:2009.08231, DOI:10.21105/joss.02807.

In particular, if you use any of the results that involve Pencil Code simulations, please cite the Pencil Code paper and the code, as well as the original work.

Routines

The main routines of cosmoGW are stored under src/cosmoGW:

• GW_back.py: functions relevant for cosmological stochastic gravitational wave backgrounds (SGWB).
• cosmology.py: functions relevant for cosmological calculations, including a Friedmann solver (see tutorial on Friedmann equations in cosmology.ipnyb) that can generate the solution files being read in some Pencil Code simulations (see tutorial cosmology_PC.ipnyb).
• cosmoMF.py: functions relevant for cosmological magnetic fields like bounds from different experiments, observations or projected sensitivities, and expectations from theory, among others. Coming soon!
• GW_analytical.py: contains analytical calculations and useful mathematical functions
• GW_models.py: models to describe the GW background produced from magnetic and velocity field perturbations in the primordial plasma, e.g., induced by a first-order phase transition. It includes models to describe the GW background from MHD turbulence, from sound waves, and from non-linear compressional motion.
• GW_templates.py: contains templates to describe the GW background from different sources
• hydro_bubbles.py: functions to compute fluid perturbations induced by the expansion of bubbles in first-order phase transitions
• interferometry.py: functions to compute the response and sensitivity functions of interferometer space-based GW detectors (e.g., LISA and Taiji) to the detection of SGWBs (see tutorial on LISA interferometry in interferometry.ipynb) energy density and polarization, including the space-based network LISA-Taiji to detect polarization.
• reading.py: functions to read the output files of a specific set of runs (project) of the Pencil Code.
• spectra.py: contains description for specific spectral templates, postprocessing routines for numerical spectra, and other mathematical routines.

Resources

Some data files are available in cosmoGW that are useful in some of the projects. They are stored in src/cosmoGW/resources

• cosmology: includes files relevant for the cosmological evolution of the Universe and contains a tutorial on solving Friedmann equations.
• interferometry: includes files relevant for space-based GW interferometry calculations and contains a tutorial on computing the response functions, sensitivities and power law sensitivities to SGWB energy density and polarization.
• detector_sensitivity: includes the sensitivity of various detectors (ground-based, space-based, and pulsar timing arrays, among others), see the README file for info and references.
• higgsless: contains data sets of the simulations conducted using the Higgsless approach to model the dynamics of first-order phase transitions.

Tutorials

• GWs_sound-waves

Projects

Particular projects with Jupyter notebooks are available under projects

• GWs_from_PTs: contains tutorials related to the production of GWs (self-similar profiles calculation for now, but more coming soon!)

Publications

The work of the following publications can be reproduced using CosmoGW:

• [RoperPol:2019wvy]: Numerical Simulations of Gravitational Waves from Early-Universe Turbulence, A. Roper Pol, S. Mandal, A. Brandenburg, T. Kahaniashvili, A. Kosowsky, Phys. Rev. D 102 (2020) 8, 083512, arXiv:1903.08585. Datasets produced using Pencil Code are publicly available at doi:10.5281/zenodo.3692072. Direct access to Pencil Code files is also available in brandenb/projects/GW/.

• [RoperPol:2021xnd]: Polarization of gravitational waves from helical MHD turbulent sources, A. Roper Pol, S. Mandal, A. Brandenburg, T. Kahniashvili, J. Cosmol. Astropart. Phys. 04 (2022) 04, 019, arXiv:2107.05356. Datasets produced using Pencil Code are publicly available at doi:10.5281/zenodo.5525504.

• [RoperPol:2022iel]: Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band, A. Roper Pol, C. Caprini, A. Neronov, D. Semikoz, Phys. Rev. D 105 (2022) 12, 123502, arXiv:2201.05630. Datasets produced using Pencil Code are publicly available at doi:10.5281/zenodo.5782752.

• [He:2022qcs]: Modified propagation of gravitational waves from the early radiation era, Y. He, A. Roper Pol, A. Brandenburg, J. Cosmol. Astropart. Phys. 06 (2023) 025, arXiv:2212.06082. Datasets produced using Pencil Code are publicly available at doi:10.5281/zenodo.5525504. Direct access to Pencil Code files is also available in brandenb/projects/Horndeski/.

• [RoperPol:2023bqa]: LISA and γ-ray telescopes as multi-messenger probes of a first-order cosmological phase transition, A. Roper Pol, A. Neronov, C. Caprini, T. Boyer, D. Semikoz, submitted to Astron. Astrophys., arXiv:2307.10744.

• [RoperPol:2023dzg]: Characterization of the gravitational wave spectrum from sound waves within the sound shell model, A. Roper Pol, S. Procacci, C. Caprini, Phys. Rev. D 109 (2024) 6, 063531, arXiv:2308.12943.

• [Caprini:2024gyk]: Gravitational waves from decaying sources in strong phase transitions, A. Roper Pol, I. Stomberg, C. Caprini, R. Jinno, T. Konstandin, H. Rubira, J. High Energy Phys. 07 (2025) 217, arXiv:2409.03651.