Covariant Analysis of Experimental Constraints on the Brane-world

Four recently reported experimental constraints on brane-world models in five dimensions are analyzed under the covariant formulation of the theory. Two of them concern local gravity, reporting on the deflection of light rays by the Sun and the orbits of the binary pulsar PSR1913+16. The other two are of cosmological nature, related to brane-world cosmologies which depend on the square of the density energy. One reporting on inconsistencies of these models with the high energy inflation and the other reporting on the inconsistency of the vector perturbations resulting from the bulk, with the recent WMAP/SDSS/2dF data on the expansion of the universe. After reviewing the covariant equations of motion in arbitrary dimensions, we conclude that the extra gravitational fields resulting from linear bulk waves do not influence the covariant brane-world equations. On the other hand we find that the bending of light and the high energy inflation constraints can survive the covariant formulation. This formulation, based on a differentiable embedding structure shows that there is a dynamical relationship between the the brane-world and the bulk geometries and that the dimension of the latter cannot be fixed except when it acquires a flat and stable configuration. Together with the evidence given by the constraints, we conclude that the five-dimensional models of the brane-world face serious mathematical and experimental limitations