  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\times S^2,
to an infinite future, which is a dS_6-type spacetime with the boundary
R^3\times 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\times S^2 or an H^4 bundle over S^2. 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.
