Indistinguishable Macroscopic Behaviour of Palatini Gravities and   General Relativity
  We show that, within some modified gravity theories, such as the Palatini models, the non-linear nature of the field equations implies that the usual naive averaging procedure (replacing the microscopic energy-momentum by its cosmological average) could be invalid. As a consequence, the relative motion of particles in Palatini theories is actually indistinguishable from that predicted by General Relativity. Moreover, there is no WEP violation. Our new and most important result is that the cosmology and astrophysics, or put more generally, the behaviours on macroscopic scales, predicted by these two theories are the same, and as a result the naturalness problems associated with the cosmological constant are not alleviated. Palatini gravity does however predict alterations to the internal structure of particles and the particle physics laws, e.g., corrections to the hydrogen energy levels. Measurements of which place strong constraints on the properties of viable Palatini gravities. 
Baojiu Li, David F. Mota, Douglas J. Shaw