  We identify a time-dependent class of metrics with potential applications to
cosmology, which emerge from negative-tension branes. The cosmology is based on
a general class of solutions to Einstein-dilaton-Maxwell theory, presented in
{hep-th/0106120}. We argue that solutions with hyperbolic or planar symmetry
describe the gravitational interactions of a pair of negative-tension
$q$-branes. These spacetimes are static near each brane, but become
time-dependent and expanding at late epoch -- in some cases asymptotically
approaching flat space. We interpret this expansion as being the spacetime's
response to the branes' presence. The time-dependent regions provide explicit
examples of cosmological spacetimes with past horizons and no past naked
singularities. The past horizons can be interpreted as S-branes. We prove that
the singularities in the static regions are repulsive to time-like geodesics,
extract a cosmological `bounce' interpretation, compute the explicit charge and
tension of the branes, analyse the classical stability of the solution (in
particular of the horizons) and study particle production, deriving a general
expression for Hawking's temperature as well as the associated entropy.
