OGCOSMO: An auxiliary tool for the study of the Universe within hierarchical scenario of structure formation

In this work is presented the software OGCOSMO. This program was written using high level design methodology (HLDM), that is based on the use of very high level (VHL) programing language as main, and the use of the intermediate level (IL) language only for the critical processing time. The languages used are PYTHON (VHL) and FORTRAN (IL). The core of OGCOSMO is a package called OGC{_}lib. This package contains a group of modules for the study of cosmological and astrophysical processes, such as: comoving distance, relation between redshift and time, cosmic star formation rate, number density of dark matter haloes and mass function of supermassive black holes (SMBHs). The software is under development and some new features will be implemented for the research of stochastic background of gravitational waves (GWs) generated by: stellar collapse to form black holes, binary systems of SMBHs. Even more, we show that the use of HLDM with PYTHON and FORTRAN is a powerful tool for producing astrophysical softwares.

💡 Research Summary

The paper presents OGCOSMO, a software framework designed to facilitate quantitative studies of cosmology and hierarchical structure formation. The authors adopt a High‑Level Design Methodology (HLDM) that combines a very‑high‑level language (Python) for overall program flow and user interaction with an intermediate‑level language (Fortran) for computationally intensive kernels. This dual‑language strategy leverages Python’s extensive scientific ecosystem, readability, and rapid prototyping capabilities while exploiting Fortran’s superior performance for large‑scale numerical integration, differential equation solving, and array‑based calculations. The interface between the two languages is realized through f2py/Cython wrappers, allowing seamless exchange of NumPy arrays and minimizing data‑copy overhead; Fortran subroutines are parallelized with OpenMP and are prepared for future GPU acceleration.

The core of OGCOSMO is the OGC_lib package, which currently implements four major modules: (1) Cosmological distance and redshift‑time conversion utilities based on ΛCDM parameters, employing high‑precision numerical integration to compute comoving, luminosity, and angular‑diameter distances; (2) Cosmic star‑formation‑rate (SFR) calculators that combine observed galaxy luminosity functions with mass‑to‑light ratios, supporting multiple empirical SFR prescriptions (e.g., Madau‑Dickinson, Behroozi) for flexible modeling of galaxy evolution; (3) Dark‑matter halo number‑density and mass‑function estimators using Press‑Schechter and Sheth‑Tormen formalisms, providing halo abundances as functions of mass and redshift; and (4) Supermassive black‑hole (SMBH) mass‑function tools that incorporate observed M–σ relations and growth channels (gas accretion, mergers) to predict SMBH number densities and evolutionary tracks.

A key future direction highlighted by the authors is the implementation of a stochastic gravitational‑wave (GW) background module. This component will model two principal GW sources: (i) stellar‑collapse–induced black‑hole formation, where the event rate is derived from the redshift‑dependent SFR and an initial mass function, and (ii) SMBH binary mergers, whose coalescence rate will be generated via Monte‑Carlo realizations of halo merger trees combined with the SMBH mass function. For each source class, the software will compute the characteristic strain and energy density spectrum Ω_GW(f) by integrating over redshift and source parameters, using state‑of‑the‑art waveform models (e.g., PhenomD).

From a software engineering perspective, OGCOSMO’s modular architecture enables straightforward incorporation of new physics (alternative dark‑energy equations of state, modified gravity, non‑standard initial conditions) and the ingestion of up‑to‑date observational datasets (e.g., JWST high‑z galaxy catalogs, Euclid weak‑lensing maps). The Python front‑end provides interactive Jupyter‑Notebook support, Matplotlib/Plotly visualizations, and an intuitive API for parameter sweeps, while the Fortran back‑end ensures that heavy numerical workloads remain tractable on multi‑core CPUs.

The authors conclude that the combination of HLDM with Python and Fortran constitutes a powerful paradigm for astrophysical software development. OGCOSMO already offers a functional suite for distance measures, SFR, halo statistics, and SMBH demographics, and its planned extensions—particularly the GW background module, Bayesian parameter inference tools, and high‑performance I/O—will position it as a comprehensive platform for researchers investigating the formation and evolution of cosmic structures across a wide range of scales.