Breaking diffeomorphism invariance and tests for the emergence of gravity

If general relativity is an emergent phenomenon, there may be small violations of diffeomorphism invariance. We propose a phenomenology of perturbatively small violations of general relativity by the inclusion of terms which break general covariance. These can be tested by matching to the Parameterized Post Newtonian (PPN) formalism. The most sensitive tests involve pulsar timing and provide an extremely strong bound, with a dimensionless constraint of order 10−20 relative to gravitational strength