Microscopic and Macroscopic Behaviors of Palatini Modified Gravity Theories

TL;DR

This paper investigates how averaging procedures in Palatini modified gravity theories affect classical and quantum phenomena, revealing that while classical predictions align with general relativity, quantum and electromagnetic effects could differ, offering new observational constraints.

Contribution

It clarifies the correct averaging method in Palatini gravity and explores its implications for particle physics, photon propagation, and cosmology, highlighting differences from general relativity.

Findings

Classical masses and geodesics are indistinguishable from GR with a cosmological constant.

Electromagnetic fields require a different averaging, affecting photon propagation.

Palatini theories can cause measurable shifts in hydrogen energy levels.

Abstract

We show that, within modified gravity, the non-linear 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 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, 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 behaviour of a Universe dominated by radiation. Finally, Palatini theories also predict alterations to particle physics laws. For example, it 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