  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.
