Solar System planetary motions and modified gravity

According to the braneworld model of gravity by Dvali, Gabadadze and Porrati, our Universe is a four-dimensional space-time brane embedded in a larger, infinite five-dimensional bulk space. Contrary to the other forces constrained to remain on the brane, gravity is able to explore the entire bulk getting substantially modified at large distances. This model has not only cosmological consequences allowing to explain the observed acceleration of the expansion of our Universe without resorting to the concept of dark energy, but makes also testable predictions at small scales. Interestingly, such local effects can yield information on the global properties of the Universe and on the kind of expansion currently ongoing. Indeed, among such predictions there are extra precessions of the perihelia and the mean longitudes of the planetary orbits which are affected by a twofold degeneration sign: one sign refers to a Friedmann-LemâıtreRobertson-Walker phase while the opposite sign is for a self-sccelerated phase. In this paper we report on recent observations of planetary motions in the Solar System which are compatible with the existence of a fifth dimension as predicted in the Dvali-Gabadadze-Porrati model with a self-accelerated cosmological phase, although the errors are still large. The Friedmann-LemâıtreRobertson-Walker phase is, instead, ruled out.