Modeling the Cosmological Lyman- α Forest at the Field Level

The distribution of absorption lines in the spectra of distant quasars, called the Lyman-α (Ly-α) forest, is a unique probe of cosmology and the intergalactic medium at high redshifts and small scales. The statistical power of ongoing redshift surveys demands precise theoretical tools to model the Ly-α forest. We address this challenge by developing an analytic, perturbative forward model to predict the Ly-α forest at the field level for a given set of cosmological initial conditions. Our model shows a remarkable performance when compared with the Sherwood hydrodynamic simulations: it reproduces the Ly-α forest flux power spectrum, its cross-correlation with dark matter halos, and the one-point probability distribution function of both fields at the percent level down to scales of a few Mpc. Our work provides crucial tools that bridge analytic modeling on large scales with simulations on small scales, enabling field-level inference from Ly-α forest data and simulation-based priors for cosmological analyses. This is especially timely for realizing the full scientific potential of the Ly-α forest measurements by the dark energy spectroscopic instrument.