  In this paper we establish dualities between inflationary, cyclic/ekpyrotic,
and phantom cosmologies within the patch formalism approximating high-energy
effects in scenarios with extra dimensions. The exact dualities relating the
four-dimensional spectra are broken in favour of their braneworld counterparts;
the dual solutions display new interesting features because of the modification
of the effective Friedmann equation on the brane. We then address some
qualitative issues about phantomlike cosmologies without phantom matter.
