We study cosmological properties of type IIA compactifications on orientifolds of SU(3)-structure manifolds with non-vanishing geometric flux. These compactifications give rise to effective 4D N = 1 supergravity theories that do not fall under some recentlyproven no-go theorems against de Sitter vacua and slow-roll inflation. Focusing on a wellunderstood class of models based on coset spaces, however, we can use a refined no-go theorem that rules out de Sitter vacua and slow-roll inflation in all but one case. The refined no-go theorem uses the dilaton and a specific linear combination of the Kähler moduli, which is different from the overall volume modulus. It puts a lower bound on the first slow-roll parameter: ǫ ≥ 2. The only case not ruled out is the manifold SU(2)×SU(2), for which we indeed find critical points with ǫ numerically zero. However, all the points we could find have a tachyon corresponding to an eta-parameter η −2.4.

We consider string theory compactifications of the form AdS 4 ×M 6 with orientifold six-planes, where M 6 is a six-dimensional compact space that is either a nilmanifold or a coset. For all known solutions of this type we obtain the four-dimensional N = 1 low energy effective theory by computing the superpotential, the Kähler potential and the mass spectrum for the light moduli. For the nilmanifold examples we perform a cross-check on the result for the mass spectrum by calculating it alternatively from a direct Kaluza-Klein reduction and find perfect agreement. We show that in all but one of the coset models all moduli are stabilized at the classical level. As an application we show that all but one of the coset models can potentially be used to bypass a recent no-go theorem against inflation in type IIA theory.

Abstract:We construct new families of non-supersymmetric sourceless type IIA AdS 4 vacua on those coset manifolds that also admit supersymmetric solutions. We investigate the spectrum of left-invariant modes and find that most, but not all, of the vacua are stable under these fluctuations. Generically, there are also no massless moduli. * Postdoctoral Fellow FWO -Vlaanderen.

This is a summary of [1], where the low energy effective theory of type IIA AdS4 N = 1 flux compactifications on nilmanifolds and cosets has been analyzed.