Modelling the redshift-space cluster-galaxy correlation function on Mpc scales with emulation of the pairwise velocity distribution

We present a method for modelling the cluster-galaxy correlation function in redshift-space, down to ~ Mpc scales. The method builds upon the so-called Galaxy Infall Kinematics (GIK) model, a parametric model for the pairwise velocities of galaxies with respect to nearby galaxy clusters. We fit the parameters of the GIK model to a suite of simulations run with different cosmologies, and use Gaussian Processes to emulate how the GIK parameters depend upon cosmology. This emulator can then be combined with knowledge of the real-space clustering of clusters and galaxies, to predict the cluster-galaxy correlation function in redshift space. Fitting this model to an observed correlation function enables the extraction of cosmological parameter constraints, and we present forecasts for a DESI-like survey. We also perform tests of the robustness of our constraints from fitting to mock data extracted from N-body simulations, finding that fitting to scales < 3 Mpc/h leads to a biased inference on cosmology, due to model misspecification on these scales. Finally, we discuss what steps will need to be taken in order to apply our method to real data.