Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes

Abstract

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 $\mathcal{N}=1$ supersymmetry. Our derivation is based on the dilaton, K\"ahler 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 $ϵ$ 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 $ϵ$ can indeed be achieved. We stress that there seems to be an $\ensuremath{\eta}$-problem, 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 ${\ensuremath{\alpha}}^{\ensuremath{'}}$-expansion.