Simple cosmological de Sitter solutions on dS$_4 \times Y_6$ spaces
  Explicit time-dependent solutions of the 10D vacuum Einstein equations are
found for which spacetime is compactified on six-dimensional warped spaces. We
explicitly work out an example where the internal manifold is a six-dimensional
generalized space having positive, negative or zero scalar curvature, whose
base can be a five-sphere $S^5$ or an Einstein space $T^{1,1}=(S^2\times
S^2)\rtimes S^1$. In this paper, inflationary de Sitter solutions are found
just by solving the 10D vacuum Einstein equations. Our results further show
that the limitation with warped models studied to date has arisen partly from
an oversimplification of the 10D metric ansatz. We also give some explicit
examples of a non-singular warped compactification on de Sitter space dS$_4$.
