Field-level Lyman-alpha forest modelling in redshift space via augmented non-local Fluctuating Gunn-Peterson Approximation

We present an improved analytical model to predict the Lyman-alpha forest at the field level in redshift space from the dark matter field, expanding upon the widely-used Fluctuating Gunn-Peterson approximation (FGPA). In particular, we introduce the dependence on the cosmic web environment (knots, filaments, sheets, voids) in the model, thereby effectively accounting for non-local bias. Furthermore, we include a detailed treatment of velocity bias in the redshift space distortions modelling, allowing the velocity bias to be cosmic-web dependent. We find evidence for a significant difference of the same model parameters in different environments, suggesting that for the investigated setup the simple standard FGPA is not able to adequately predict the Lyman-alpha forest in the different cosmic web regimes. We reproduce the summary statistics of the reference cosmological hydrodynamic simulation we use for comparison, yielding accurate mean transmitted flux, probability distribution function, 3D power spectrum, and bispectrum. In particular, we achieve maximum deviation and average deviations accuracy in the Lyman-alpha forest 3D power spectrum of $\sim 3\%$ and $\sim 0.1\%$ up to $k\sim 0.4 \, h \, {\rm Mpc}^{-1}$, $\sim 5\%$ and $\sim 1.8\%$ up to $k \sim 1.4 \, h \, {\rm Mpc}^{-1}$. Our new model outperforms previous analytical efforts to predict the Lyman-alpha forest at the field level in all the probed summary statistics, and has the potential to become instrumental in the generation of fast accurate mocks for covariance matrices estimation in the context of current and forthcoming Lyman-alpha forest surveys.