From de Sitter to de Sitter -: art. no. 004

We obtain D = 6, N = (1, 1) de Sitter supergravity from a hyperbolic reduction of the massive type IIA* theory. We construct a smooth cosmological solution in which the co-moving time runs from an infinite past, which is dS(4) x S-2, to an infinite future, which is a dS(6)-type spacetime with the boundary R-3 x S-2. This provides an effective four-dimensional cosmological model with two compact extra dimensions forming an S-2. Interestingly enough, although the solution is time dependent, it arises from a first-order system via a superpotential construction. We lift the solutions back to D = 10, and in particular obtain two smooth embeddings of dS(4) in massive type IIA*, with the internal space being either H-4 x S-2 or an H-4 bundle over S-2. We also obtain the analogous D = 5 and 4 solutions. We show that there exist cosmological solutions that describe an expanding universe with the expansion rate significantly larger in the past than in the future.