Field-level forward modelling with a physical, non-local stochastic galaxy-bias model calibrated to hydrodynamical simulations

Abstract

Galaxy positions and shapes, as tracers of the large-scale structure of the Universe, are key observables for testing cosmological models in the late Universe and into the non-linear regime. In this context, multi-scale baryonic dynamics, and their evolution over time, can have considerable effects on the galaxy-halo connection (galaxy bias). If unmodelled, residual uncertainties in the galaxy field can obstruct cosmological inference and weaken tests of extensions to $\Lambda$CDM. In two-dimensional projection along the line-of-sight, the relevant halo-level information can be incomplete or effectively marginalised over, motivating bias models that remain predictive without detailed halo-internal parameterisations. To this end, I will present a new analytic galaxy-bias model in projection that incorporates stochasticity and non-locality already at linear order, while enforcing physicality and statistical isotropy for galaxy fields constructed from an underlying matter field on the sphere. This yields an explicit decomposition into a linear, non-local stochastic component in harmonic space and a non-linear residual. I will show how the model can be calibrated to the projected power spectrum measured in large-volume hydrodynamical simulations (e.g. FLAMINGO) to sample galaxy populations from simulated matter fields while conditioning on selected galaxy properties, such as halo mass or redshift. The model matches the two-point statistics down to the simulations’ resolution by construction, while recovering the bispectrum down to $\sim$10 Mpc for $M_{\mathrm{h}} > 10^{13} \, M_{\odot}$ from redshift 0.05 to 3. The model better reproduces non-linearities driven by correlations between the local amplitude of the galaxy field and its phase, as well as the field’s mode coupling, than a local bias model across most scales and down to $M_{\mathrm{h}} = 10^{11} \, M_{\odot}$. This improves the robustness of joint clustering plus galaxy-galaxy lensing consistency tests of the growth of structure, helping to separate astrophysical systematics from genuine scale-dependent structure growth. Finally, I will demonstrate how this framework enables efficient field-level forward modelling of galaxy positions consistent with hydrodynamical simulations, while varying cosmological and astrophysical parameters, providing a practical route towards simulation-based inference (with a few of milliseconds per model evaluation) and principled model comparison with forthcoming surveys such as Euclid, Rubin LSST, and DESI.