We explore in detail the prospects of obtaining a four-dimensional de Sitter
universe in classical supergravity models with warped and time-independent
extra dimensions, presenting explicit cosmological solutions of the
(4+n)-dimensional Einstein equations with and without a bulk cosmological
constant term. For the first time in the literature we show that there may
exist a large class of warped supergravity models with a noncompact extra
dimension which lead to a finite 4D Newton constant as well as a massless 4D
graviton localised on an inflating four-dimensional FLRW universe. This result
helps establish that the `no-go' theorem forbidding acceleration in `standard'
compactification of string/M-theory on physically compact spaces should not
apply to a general class of warped supergravity models that allows at least one
noncompact direction. We present solutions for which the size of the radial
dimension takes a constant value in the large volume limit, providing an
explicit example of spontaneous compactification.Comment: 19 pages, 2 figures; final (journal) versio
