Microscopic and macroscopic behaviors of Palatini modified gravity theories

We show that, within modified gravity, the nonlinear nature of the field equations implies that the usual naive averaging procedure (replacing the microscopic energy-momentum by its cosmological average) is invalid. We discuss then how the averaging should be performed correctly and show that, as a consequence, at the classical level the physical masses and geodesics of particles, cosmology, and astrophysics in Palatini modified gravity theories are all indistinguishable from the results of general relativity plus a cosmological constant. Palatini gravity is, however, a different theory from general relativity and predicts different internal structures of particles from the latter. On the other hand, and in contrast to classical particles, the electromagnetic field permeates in the space, and hence a different averaging procedure should be applied here. We show that, in general, Palatini gravity theories would then affect the propagation of photons, thus changing the behavior of a Universe dominated by radiation. Finally, Palatini theories also predict alterations to particle physics laws. For example, they can lead to sensitive corrections to the hydrogen energy levels, the measurements of which could be used to place very strong constraints on the properties of viable Palatini gravity theories.