ForestFlow: predicting the Lyman-α forest clustering from linear to nonlinear scales

¹ Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, 08193 Bellaterra (Barcelona), Spain
² Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain
³ Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
⁴ Physics Dept., Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA
⁵ Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy
⁶ Department of Physics & Astronomy, University College London, Gower Street, London WC1E 6BT, UK
⁷ Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
⁸ Instituto de Física, Universidad Nacional Autónoma de México, Cd. de México C.P. 04510, Mexico
⁹ University of California, Berkeley, 110 Sproul Hall #5800, Berkeley, CA 94720, USA
¹⁰ Departamento de Física, Universidad de los Andes, Cra. 1 No. 18A-10, Edificio Ip, CP 111711 Bogotá, Colombia
¹¹ Observatorio Astronómico, Universidad de los Andes, Cra. 1 No. 18A-10, Edificio H, CP 111711 Bogotá, Colombia
¹² Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain
¹³ Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth PO1 3FX, UK
¹⁴ Fermi National Accelerator Laboratory, PO Box 500 Batavia, IL 60510, USA
¹⁵ Center for Cosmology and AstroParticle Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, OH 43210, USA
¹⁶ Department of Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, OH 43210, USA
¹⁷ The Ohio State University, Columbus, 43210 OH, USA
¹⁸ Department of Physics, Southern Methodist University, 3215 Daniel Avenue, Dallas, TX 75275, USA
¹⁹ Department of Physics and Astronomy, University of California, Irvine 92697, USA
²⁰ Departament de Física, Serra Húnter, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
²¹ Department of Astronomy, The Ohio State University, 4055 McPherson Laboratory, 140 W 18th Avenue, Columbus, OH 43210, USA
²² Institució Catalana de Recerca i Estudis Avançats, Passeig de Lluís Companys, 23, 08010 Barcelona, Spain
²³ Departamento de Física, Universidad de Guanajuato – DCI, C.P. 37150 Leon, Guanajuato, Mexico
²⁴ Instituto Avanzado de Cosmología A. C., San Marcos 11 – Atenas 202. Magdalena Contreras, 10720 Ciudad de México, Mexico
²⁵ Departament de Física, EEBE, Universitat Politècnica de Catalunya, c/Eduard Maristany 10, 08930 Barcelona, Spain
²⁶ Department of Physics and Astronomy, Sejong University, Seoul 143-747, Korea
²⁷ CIEMAT, Avenida Complutense 40, E-28040 Madrid, Spain
²⁸ Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
²⁹ NSF NOIRLab, 950 N. Cherry Ave., Tucson, AZ 85719, USA

^⋆ Corresponding author; jchaves@ifae.es

Received: 28 August 2024
Accepted: 7 January 2025

Abstract

On large scales, the Lyman-α forest provides insights into the expansion history of the Universe, while on small scales, it imposes strict constraints on the growth history, the nature of dark matter, and the sum of neutrino masses. This work introduces ForestFlow, a novel framework that bridges the gap between large- and small-scale analyses, which have traditionally relied on distinct modeling approaches. Using conditional normalizing flows, ForestFlow predicts the two Lyman-α linear biases (b_δ and b_η) and six parameters describing small-scale deviations of the three-dimensional flux power spectrum (P_3D) from linear theory as a function of cosmology and intergalactic medium physics. These are then combined with a Boltzmann solver to make consistent predictions, from arbitrarily large scales down to the nonlinear regime, for P_3D and any other statistics derived from it. Trained on a suite of 30 fixed-and-paired cosmological hydrodynamical simulations spanning redshifts from z = 2 to 4.5, ForestFlow achieves 3 and 1.5% precision in describing P_3D and the one-dimensional flux power spectrum (P_1D) from linear scales to k = 5 Mpc⁻¹ and k_∥ = 4 Mpc⁻¹, respectively. Thanks to its conditional parameterization, ForestFlow shows similar performance for ionization histories and two ΛCDM model extensions – massive neutrinos and curvature – even though none of these are included in the training set. This framework will enable full-scale cosmological analyses of Lyman-α forest measurements from the DESI survey.