Probing theories of gravity with phase space-inferred potentials of galaxy clusters

Modified theories of gravity provide us with a unique opportunity to generate innovative tests of gravity. In Chameleon f(R) gravity, the gravitational potential differs from the weak-field limit of general relativity (GR) in a mass dependent way. We develop a probe of gravity which compares high mass clusters, where Chameleon effects are weak, to low mass clusters, where the effects can be strong. We utilize the escape velocity edges in the radius/velocity phase space to infer the gravitational potential profiles on scales of 0.3–1 virial radii. We show that the escape edges of low mass clusters are enhanced compared to GR, where the magnitude of the difference depends on the background field value |f_R0|. We validate our probe using N-body simulations and simulated light cone galaxy data. For a Dark Energy Spectroscopic Instrument Bright Galaxy Sample, including observational systematics, projection effects, and cosmic variance, our test can differentiate between GR and Chameleon f(R) gravity models,  |f_R0|=4×10⁻⁶ (2×10⁻⁶) at >5σ (>2σ), more than an order of magnitude better than current cluster-scale constraints.