From de Sitter to de Sitter

الأصل · EN

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 dS₄× S², to an infinite future, which is a dS₆-type spacetime with the boundary R³× S². This provides an effective four-dimensional cosmological model with two compact extra dimensions forming an S². 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 dS₄ in massive type IIA*, with the internal space being either H⁴× S² or an H⁴ bundle over S². We also obtain the analogous D=5 and D=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.