  We study Randall-Sundrum two brane setups with mismatched brane tensions. For
the vacuum solutions, boundary conditions demand that the induced metric on
each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For
incompatible boundary conditions, the bulk metric is necessarily
time-dependent. This introduces a new class of time-dependent solutions with
the potential to address cosmological issues and provide alternatives to
conventional inflationary (or contracting) scenarios. We take a first step in
this paper toward such solutions. One important finding is that the resulting
solutions can be very succinctly described in terms of an effective action
involving only the induced metric on either one of the branes and the radion
field. But the full geometry cannot necessarily be simply described with a
single coordinate patch. We concentrate here on the time-dependent solutions
but argue that supplemented with a brane stabilization mechanism one can
potentially construct interesting cosmological models this way. This is true
both with and without a brane stabilization mechanism.
