On Slow-roll Moduli Inflation in Massive IIA Supergravity with Metric Fluxes

TL;DR

This work extends no-go theorems for slow-roll inflation in string compactifications to massive IIA setups with metric fluxes, incorporating dilaton, Kähler, and complex-structure moduli in the four-dimensional ${\cal N}=1$ EFT. By deriving bounds on the slow-roll parameter $ε$ from the moduli-dependent scalar potential and exploring toroidal orientifolds, it shows that most models yield $ε$ of order unity under the Bianchi identities, effectively ruling out slow-roll inflation and even de Sitter extrema in these backgrounds. Only two ${\mathbb Z}_2\times{\mathbb Z}_2$ toroidal cases avoid the strongest bounds, and numerical scans reveal an accompanying $η$-problem and tachyonic directions, indicating that extended inflation is cosmologically unviable in this class at large volume and small string coupling. The results highlight the essential role of metric fluxes and residual duality symmetries in constraining the landscape of string inflationary solutions, and point to the need for correcting effects beyond leading order or considering non-geometric fluxes or backreacted branes to pursue viable models.

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 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 εis 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 εcan indeed be achieved. We stress that there seems to be an η-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 α'-expansion.