Flow equations in generalized braneworld scenarios

We discuss the flow equations in the context of general braneworld cosmologies with a modified Friedmann equation, for either an ordinary scalar field or a Dirac–Born–Infeld tachyon as inflaton candidates. The 4D, Randall–Sundrum, and Gauss–Bonnet cases are compared, using the patch formalism which provides a unified description of these models. The inflationary dynamics is described by a tower of flow parameters that can be evolved in time to select a particular subset of points in the space of cosmological observables. We analyze the stability of the fixed points in all the cosmologies (our results in the 4D case already extending those in the literature). Numerical integration of the flow equations shows that the predictions of the Gauss–Bonnet braneworld differ significantly as compared to the Randall–Sundrum and 4D scenarios, whereas tachyon inflation gives tensor perturbations smaller than those in the presence of a normal scalar field. These results are extended to the realization of a noncommutative space-time preserving maximal symmetry. In this case the tensor-to-scalar signal is unchanged, while blue-tilted spectra are favoured.