An emulation-based model for the projected correlation function

Data from the ongoing Euclid survey will map out billions of galaxies in the Universe, covering more than a third of the sky. This data will provide a wealth of information about the large-scale structure of the Universe and will have a significant impact on cosmology in the coming years. In this paper we introduce an emulator-based halo model approach to forward-modeling the relationship between cosmological parameters and the projected galaxy-galaxy two-point correlation function (2PCF). Utilizing the large AbacusSummit simulation suite, we emulated the 2PCF by generating mock-galaxy catalogs within the halo occupation distribution (HOD) framework. Our emulator is designed to predict the 2PCF over scales $0.1 ≤ r / (h^ Mpc ) ≤ 105$, from which we derived the projected correlation function, independent of redshift space distortions. We demonstrate that the emulator accurately predicts the projected correlation function over scales $0.5 ≤ r_⊥/(h^ Mpc ) ≤ 40$ given a set of cosmological and HOD parameters. We then employed this model in a parameter inference analysis, showcasing its ability to constrain cosmological parameters. Our findings indicate that the projected correlation function places only weak constraints on several cosmological parameters due to its intrinsic lack of information; additional clustering statistics are necessary to better probe the underlying cosmology. Despite the simplified covariance matrix used in the likelihood model, the posterior distributions of several cosmological parameters remain broad, underscoring the need for a more comprehensive approach.