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 N = 1 supersymmetry. Our derivation is based on the dilaton, Kähler 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 ǫ 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 ǫ can indeed be achieved. We stress that there seems to be an η-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 α ′ -expansion.

Inflation and String Theory

“…In stabilized flux compactifications of type IIA string theory [498][499][500], in contrast, complex structure moduli could a priori be natural inflaton candidates. However, in the best-understood classes of type IIA compactifications, there are no-go theorems for inflation [501,502] (see also [503]). As a result, it appears difficult to construct explicit scenarios for inflation driven by complex structure moduli.…”

Affleck-Dine baryogenesis in effective supergravity

“…The problem of obtaining Hubble-induced supersymmetry breaking terms should thus be formulated in the language of type IIA string theory, where obtaining models of inflation is difficult [27]. We will simply give an outline of how it may be possible to obtain tachyonic Hubble-induced masses.…”

De Sitter vacua from a D-term generated racetrack uplift

“…Motivated by this setup, there were many attempts constructing dS vacua [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Using the necessary constraint for the extrema [43,44] and for the stability [45], we see that the existence of minima requires not only negative curvature, but also the presence of orientifold planes.…”