Einstein static universe as a brane in extra dimensions

We present a brane-world scenario in which two regions of AdS5 space-time are glued together along a 3-brane with constant positive curvature such that all spatial dimensions form a compact manifold of topology S4. 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 RU 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 << r << RU 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∼ RU 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. (author)