  We derive several no-go theorems in the context of massive type IIA string
theory compactified to four dimensions in a way that, in the absence of fluxes,
preserves N=1 supersymmetry. Our derivation is based on the dilaton, Kaehler
and complex structure moduli dependence of the potential of the
four-dimensional effective field theory, that is generated by the presence of
D6-branes, O6-planes, RR-fluxes, NSNS 3-form flux, and geometric fluxes. To
demonstrate the usefulness of our theorems, we apply them to the most commonly
studied class of toroidal orientifolds. We show that for all but two of the
models in this class the slow-roll parameter \epsilon is bounded from below by
numbers of order unity as long as the fluxes satisfy the Bianchi identities,
ruling out slow-roll inflation and even the existence of de Sitter extrema in
these models. For the two cases that avoid the no-go theorems, we provide some
details of our numerical studies, demonstrating that small \epsilon can indeed
be achieved. We stress that there seems to be an \eta-problem, however,
suggesting that none of the models in this class are viable from a cosmological
point of view at least at large volume, small string coupling, and leading
order in the \alpha'-expansion.
