Patch dualities and remarks on nonstandard cosmologies

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 favor 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.