ON IMPLICATIONS OF EQUIVALENCE PRINCIPLE FOR MODIFIED GRAVITY THEORIES

One of the manifestations of Einstein Equivalence Principle (EEP) is that a freely falling particle in a gravitational field is following a geodesic. In Einstein's general relativity (GR) this is built in the formulation by assuming the connection to be the Levi-Civita connection. The latter may, however, be demanded to be implied by the dynamics of a generic modified gravity theory, within the Palatini formulation. We show that for extensions of the Einstein GR which are described by a Lagrangian L - L(g(mu nu), R-mu alpha beta nu), where g(mu nu) is the metric and R-mu alpha beta nu is the Riemann curvature tensor, this manifestation of EEP is only fulfilled for a special class of Lagrangians, the Lovelock gravity theories. Our analysis also implies that within the above mentioned set of modified gravity theories only for Lovelock gravity theories metric and Palatini formulations are equivalent.