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 |fR0|. We validate our probe using N-body
simulations and simulated light cone galaxy data. For a DESI (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, |fR0| = 4e-6 (2e-6)
at > 5{\sigma} (> 2{\sigma}), more than an order of magnitude better than
current cluster-scale constraints.
