The Quijote simulations

Abstract: The Quijote simulations are a set of 44,100 full N-body simulations spanning more than 7,000 cosmological models in the ${\Omega_{\rm m}, \Omega_{\rm b}, h, n_s, \sigma_8, M_\nu, w }$ hyperplane. At a single redshift the simulations contain more than 8.5 trillions of particles over a combined volume of 44,100 $(h^{-1}{\rm Gpc})^3$; each simulation follow the evolution of $256^3$, $512^3$ or $1024^3$ particles in a box of $1~h^{-1}{\rm Gpc}$ length. Billions of dark matter halos and cosmic voids have been identified in the simulations, whose runs required more than 35 million core hours. The Quijote simulations have been designed for two main purposes: 1) to quantify the information content on cosmological observables, and 2) to provide enough data to train machine learning algorithms. In this paper we describe the simulations and show a few of their applications. We also release the Petabyte of data generated, comprising hundreds of thousands of simulation snapshots at multiple redshifts, halo and void catalogs, together with millions of summary statistics such as power spectra, bispectra, correlation functions, marked power spectra, and estimated probability density functions.

An Analysis of the Quijote Simulations

The Quijote simulations represent a significant advancement in the field of cosmology, comprised of an expansive suite of 44,100 full N-body simulations designed to explore cosmological phenomena across over 7,000 different models. The primary objectives of these simulations are to quantify the information content in cosmological observables and to provide an extensive dataset for machine learning training.

Numerical Scale and Computational Requirements

The simulations encompass more than 8.5 trillion particles within a cumulative spatial volume of 44,100 cubic gigaparsecs, tracked through volumes of 1 (h^{-1}) Gpc^3. They simulate the evolution of particles at various resolutions (256^3, 512^3, and 1024^3 particles), which required over 35 million core hours to compute. This immense computational task illustrates the logistical challenge of such a comprehensive suite and presents a unique resource for cosmological research.

Applications and Data Release

The Quijote project not only simulates the large-scale structure of the universe but also identifies billions of dark matter halos and cosmic voids, utilizing a Friends-of-Friends (FoF) algorithm for halo identification. These entities are cataloged along with a variety of other statistical products derived from the simulation data, such as power spectra, bispectra, and marked power spectra. The data products extend to probability density functions of matter fields and halo fields, vastly enriching the resource available for the scientific community. To facilitate broader access and utility, the project has released a petabyte of data, making it one of the most extensive cosmological datasets available.

Methodological Advancements

Several sophisticated methods were employed within the Quijote simulations. These include the use of Zel’dovich and second-order Lagrangian perturbation theory (2LPT) to generate initial conditions, as well as separate universe simulations to account for super-sample effects. The latter technique enables a better understanding of how large-scale modes influence smaller regions, an important consideration in precision cosmology.

Implications for Cosmological Research

One significant thrust of the Quijote simulations is their role in informing and refining cosmological models. By providing detailed statistical and physical insights into potentially constraining numerous cosmological parameters, these simulations contribute towards enhancing theoretical and empirical understanding of the universe’s fundamental forces and properties, including dark energy and neutrino masses.

Machine Learning and Large-Scale Structure

The simulations offer a fertile platform for applying machine learning and deep learning techniques in cosmology. The extensive data corpus supports the training and testing of algorithms designed to uncover new, optimal statistics for extracting cosmological information, an urgent necessity given the non-Gaussian nature of cosmic structures on non-linear scales. The Quijote simulations are pivotal in mapping non-linear regime structures, advancing the computational tools that connect observed data to theoretical models.

Future Directions

Looking forward, the Quijote simulations set a precedent for future cosmological simulation projects, particularly with regards to volume scale and parameter space coverage. They underscore the importance of coupling high-resolution simulations with state-of-the-art machine learning approaches to maximize scientific returns from large-scale surveys and to prepare for upcoming missions like Euclid or the Vera C. Rubin Observatory.

In conclusion, the Quijote simulations provide an unprecedented framework for studying the universe’s large-scale structures, serving as a cornerstone resource for both analytic cosmology and computational astrophysics. They exemplify how integrated approaches combining vast simulations with advanced analytics can yield deeper insights into the fabric of the universe.