Einstein static universe as a brane in extra dimensions

We present a brane-world scenario in which two regions of AdS(5) space-time are glued together along a 3-brane with constant positive curvature such that all spatial dimensions form a compact manifold of topology S-4. It turns out that the induced geometry on the brane is given by Einstein's static universe. It is possible to achieve an anisotropy of the manifold which allows for a huge hierarchy between the size of the extra dimension R and the size of the observable universe R-U at present. This anisotropy is also at the origin of a very peculiar property of our model: the physical distance between any two points on the brane is of the order of the size of the extra dimension R regardless of their distance measured with the use of the induced metric on the brane. In an intermediate distance regime R much less than r much less than R-U gravity on the brane is shown to be effectively 4-dimensional, with corresponding large distance corrections, in complete analogy with the Randall-Sundrum II model. For very large distances r similar to R-U we recover gravity in Einstein's static universe. However, in contrast to the Randall-Sundrum II model the difference in topology has the advantage of giving rise to a geodesically complete space.