Inflationary Constraints on Type IIA String Theory

TL;DR

This paper proves that standard Calabi-Yau compactifications in type IIA string theory cannot support inflation or de Sitter vacua due to a lower bound on the slow-roll parameter, but suggests additional ingredients might enable such cosmologies.

Contribution

It establishes a no-go theorem for inflation in well-understood type IIA compactifications and discusses how adding ingredients like NS 5-branes could potentially allow inflation.

Findings

Inflation is forbidden in standard type IIA Calabi-Yau compactifications.

The slow-roll parameter epsilon >= 27/13 when V > 0, ruling out inflation.

Additional ingredients like NS 5-branes may enable inflation or de Sitter vacua.

Abstract

We prove that inflation is forbidden in the most well understood class of semi-realistic type IIA string compactifications: Calabi-Yau compactifications with only standard NS-NS 3-form flux, R-R fluxes, D6-branes and O6-planes at large volume and small string coupling. With these ingredients, the first slow-roll parameter satisfies epsilon >= 27/13 whenever V > 0, ruling out both inflation (including brane/anti-brane inflation) and de Sitter vacua in this limit. Our proof is based on the dependence of the 4-dimensional potential on the volume and dilaton moduli in the presence of fluxes and branes. We also describe broader classes of IIA models which may include cosmologies with inflation and/or de Sitter vacua. The inclusion of extra ingredients, such as NS 5-branes and geometric or non-geometric NS-NS fluxes, evades the assumptions used in deriving the no-go theorem. We focus on NS 5-branes and outline how such ingredients may prove fruitful for cosmology, but we do not provide an explicit model. We contrast the results of our IIA analysis with the rather different situation in IIB.