From de Sitter to de Sitter

Abstract

We obtain D = 6, \U0001d4a9 = (1,1) de Sitter supergravity from ahyperbolic reduction of the massive type IIA* theory. We constructa smooth cosmological solution in which the co-moving time runs froman 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 withtwo compact extra dimensions forming an S2. Interestingly enough,although the solution is time dependent, it arises from a first-ordersystem via a superpotential construction. We lift the solutionsback to D = 10, and in particular obtain two smooth embeddings ofdS4 in massive type IIA*, with the internal space being eitherH4×S2 or an H4 bundle over S2. We also obtain theanalogous D = 5 and 4 solutions. We show that there existcosmological solutions that describe an expanding universe with theexpansion rate significantly larger in the past than in the future.