On the Cosmology of Type IIA Compactifications on SU(3)-structure Manifolds

TL;DR

The paper investigates cosmology in type IIA string theory compactified on orientifolds of SU(3)-structure manifolds with geometric flux, testing the existence of de Sitter vacua and slow-roll inflation using refined no-go theorems. By applying these bounds to coset-model compactifications, it shows that all but one model are excluded from supporting viable inflation or dS phases; the remaining SU(2)×SU(2) case exhibits regions with vanishing first slow-roll parameter but harbors tachyonic directions, preventing stable dS solutions. The work clarifies the role of geometric flux, the dilaton-volume plane, and additional moduli directions in obstructing slow-roll dynamics, and it highlights the limitations of negative curvature and Romans mass as universal remedies. It also establishes a framework for evaluating future SU(3)-structure compactifications (including nil-/solvmanifolds) for cosmological viability, guiding search strategies for consistent string-inspired inflation or dark energy models.

Abstract

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 recently-proven no-go theorems against de Sitter vacua and slow-roll inflation. Focusing on a well-understood 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 Kaehler moduli, which is different from the overall volume modulus. It puts a lower bound on the first slow-roll parameter: epsilon>=2. The only case not ruled out is the manifold SU(2)x SU(2), for which we indeed find critical points with epsilon numerically zero. However, all the points we could find have a tachyon corresponding to an eta-parameter eta<= -2.4.