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The large scale infall of galaxies around massive clusters provides apotentially powerful diagnostic of structure growth, dark energy, andcosmological deviations from General Relativity. We develop and test a methodto recover galaxy infall kinematics (GIK) from measurements of theredshift-space cluster-galaxy cross-correlation function \xi_{cg}(r_p,r_\pi).Using galaxy and halo samples from the Millennium simulation, we calibrate ananalytic model of the galaxy kinematic profiles comprised of a virializedcomponent with an isotropic Gaussian velocity distribution and an infallcomponent described by a skewed 2D t-distribution with a characteristic infallvelocity v_r and separate radial and tangential dispersions. We show thatconvolving the real-space cross-correlation function with this velocitydistribution accurately predicts the redshift-space \xi_{cg}, and we show thatmeasurements of \xi_{cg} can be inverted to recover the four distinct elementsof the GIK profiles. These in turn provide diagnostics of cluster massprofiles, and we expect the characteristic infall velocity v_r(r) in particularto be insensitive to galaxy formation physics that can affect velocitydispersions within halos. As a proof of concept we measure \xi_{cg} for richgalaxy groups in the Sloan Digital Sky Survey and recover GIK profiles forgroups in two bins of central galaxy stellar mass. The higher mass bin has av_r(r) curve very similar to that of 10^{14} Msun halos in the Millenniumsimulation, and the recovered kinematics follow the expected trends with mass.GIK modeling of cluster-galaxy cross-correlations can be a valuable complementto stacked weak lensing analyses, allowing novel tests of modified gravitytheories that seek to explain cosmic acceleration.

The Redshift-Space Cluster-Galaxy Cross-Correlation Function: I. Modeling Galaxy Infall onto Millennium Simulation Clusters and SDSS Groups