Simulation-Based Priors without Simulations: an Analytic Perspective on EFT Parameters of Galaxies

Effective field theory (EFT)-based full-shape analysis with simulation-based priors (SBPs) is a novel approach to galaxy clustering data analysis, which significantly boosts the constraining power by efficiently incorporating field-level simulation information from small scales. So far, SBPs have been mostly extracted from a large set of mock catalogs generated with the Halo Occupation Distribution (HOD) approach. We show that given a halo mass function model and assuming that the EFT parameters of halos depend only on the peak height, HOD-based priors can be computed analytically for the standard 7-parameter HOD model. We derive the relevant expressions for deterministic EFT parameters from the halo model. The halo model, however, fails to accurately describe stochastic EFT parameters, for which we use a physically motivated phenomenological prescription. We compare our analytic priors with simulations and find an excellent agreement. Our approach provides analytic insights into the physics behind the EFT parameters of galaxies, and allows one to reduce the computation time of SBPs to virtually nothing. As an application, we produce a set of 100,000 EFT parameters by sampling both HOD and cosmological models, and explicitly demonstrate that any cosmology dependence can be completely absorbed by relatively minor shifts of the HOD parameters. Our approach can be generalized to other variants of the HOD and cosmological models beyond $\Lambda$CDM.