General brane geometries from scalar potentials: gauged supergravities and accelerating universes

We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. For an exponential potential we find solutions corresponding to brane geometries, generalizing the black p-branes and S-branes known for the case of vanishing potential. These geometries are singular at the origin with up to two horizons. When the singularity has negative tension or the cosmological constant is positive we find time-dependent configurations describing accelerating universes. Special cases give explicit brane geometries for gauged supergravities in various dimensions, and we discuss their interrelation. Some examples lift to give new solutions to 10D supergravity. Limiting cases preserve a fraction of the supersymmetries of the vacuum. We also consider more general potentials, including sums of exponentials. Exact solutions are found for these with up to three horizons, with potentially interesting cosmological interpretation. Further examples are provided.