Exploring the squeezed three-point galaxy correlation function with generalized halo occupation distribution models

We present the GeneRalized ANd Differentiable Halo OccupationDistribution (GRAND-HOD) routine that generalizes the standard fiveparameter halo occupation distribution (HOD) model with varioushalo-scale physics and assembly bias. We describe the methodology offour different generalizations: satellite distribution generalization,velocity bias, closest approach distance generalization, and assemblybias. We showcase the signatures of these generalizations in the 2-pointcorrelation function (2PCF) and the squeezed 3-point correlationfunction (squeezed 3PCF). We identify generalized HOD prescriptions thatare nearly degenerate in the projected 2PCF and demonstrate that thesedegeneracies are broken in the redshift-space anisotropic 2PCF and thesqueezed 3PCF. We also discuss the possibility of identifyingdegeneracies in the anisotropic 2PCF and further demonstrate the extraconstraining power of the squeezed 3PCF on galaxy-halo connectionmodels. We find that within our current HOD framework, the anisotropic2PCF can predict the squeezed 3PCF better than its statistical error.This implies that a discordant squeezed 3PCF measurement could falsifythe particular HOD model space. Alternatively, it is possible thatfurther generalizations of the HOD model would open opportunities forthe squeezed 3PCF to provide novel parameter measurements. The GRAND-HODPYTHON package is publicly available athttps://github.com/SandyYuan/GRAND-HOD.