  Some observational constraints on the brane-world based on predictions from
specific models in five dimensions, have been recently reported, both on local
and cosmological scales. In order to identify the origins of these constraints,
the equations of motion of the brane-world are translated to the most general,
model-independent (or "covariant"), formulation of the theory, based only on
the Einstein-Hilbert action for the bulk geometry, the confinement of the
standard gauge interactions and the exclusive probing of the extra dimensions
by the gravitational field. In the case of the binary pulsar PSR1913+16, it is
found that gravi-vectors and gravi-scalars do not appear in the covariant
equations, but they are replaced by vector and scalar fields related to the
extrinsic curvature of the brane-world. Only the latter one impose a condition
on the binary pulsar orbits. A general solution for this problem is proposed,
based on results from differential geometry, suggesting a stable bulk geometry,
whose existence requires higher dimensions. On the cosmological scale, it is
shown that the high energy inflation constraint originating from the square of
the energy density term in the modified Friedman's equation is mainly due to
the assumption of the reflection symmetry across the brane-world. It is shown
that this symmetry is not consistent with the regularity of the brane-world.
These results suggest that the two constraints can be lifted by increasing the
number of extra dimensions.
