Violation of the Equivalence Principle in Modified Theories of Gravity

TL;DR

This paper investigates Palatini f(R) gravity models and finds that they predict violations of the Equivalence Principle, leading to observable effects at microscopic and macroscopic scales, challenging their viability.

Contribution

It demonstrates that Palatini f(R) theories cause metric deviations near matter sources, resulting in violations of the Equivalence Principle and questioning their suitability for cosmological models.

Findings

Metrics deviate from Minkowski near matter sources

Test bodies experience structure-dependent self-accelerations

Palatini f(R) models are unlikely viable for late-time cosmic evolution

Abstract

We study modified theories of gravity of the f(R) type in Palatini formalism. For a generic f(R) lagrangian, we show that the metric can be solved as the product of a scalar function times a rank-two tensor (or auxiliary metric). The scalar function is sensitive to the local energy-momentum density. The auxiliary metric satisfies a set of equations very similar to Einstein's equations and, for weak sources, it can be approximated by the Minkowski metric. According to this, the metric coupled to the matter strongly departs from the Minkowskian one in the neighbourhood of any microscopic physical system. As a consequence, new gravitationally-induced interactions arise and lead to observable effects at microscopic and macroscopic scales. In particular, test body trajectories experience self-accelerations which depend on the internal structure and composition of the body. These facts make very unlikely the viability of Palatini f(R) models designed to change the late-time cosmic evolution.