COSMOLOGICAL EXPANSION IN THE RANDALL-SUNDRUM WARPED COMPACTIFICATION

The cosmology of a brane-universe embedded in a higher dimensional bulk spacetime presents some peculiarities not seen in ordinary (3+1) dimensional gravity. I summarize the current understanding, with emphasis on the suggestion by Randall and Sundrum that the bulk is 5-D anti-deSitter space, leading to a solution of the weak scale hierarchy problem. 1 Large Versus Small Extra Dimensions In the last few years there has been a revival of interest in the idea of extra dimensions, first proposed by Kaluza and Klein. The new realization of Arkani-Hamed, Dvali and Dimopoulos (ADD) was that the extra dimensions could be macroscopically large if one assumed that our (3 + 1) dimensional universe is a slice (a 3-brane) of the higher dimensional bulk. 1 The particles of the standard model should be restricted to the brane so that no light Kaluza-Klein (KK) excitations exist, which otherwise would have already been seen. Gravity, however, can propagate in the extra bulk dimensions (otherwise they would have no observable consequences whatsoever). The effect of the extra dimensions can only be seen on distance scales less than the order of their size. With N extra compact dimensions of size R, Newton’s gravitational force law for two masses m1 and m2, separated by a distance r, is modified to F = Γ(3+N