  The recent proposal by Hawking and Turok for obtaining an open inflationary
universe from singular instantons makes use of low-energy effective Lagrangians
describing gravity coupled to scalars and non-propagating antisymmetric
tensors. In this paper we derive some exact results for Lagrangians of this
type, obtained from spherical compactifications of M-theory and string theory.
In the case of the S^7 compactification of M-theory, we give a detailed
discussion of the cosmological solutions. We also show that the
lower-dimensional Lagrangians admit domain-wall solutions, which preserve one
half of the supersymmetry, and which approach AdS spacetimes near their
horizons.
