# No inflation in type IIA strings on rigid CY spaces

## TL;DR

This study examines flux compactifications of type IIA strings on rigid Calabi-Yau spaces, concluding that such models cannot support viable inflation due to runaway potentials and decompactification issues.

## Contribution

It provides a detailed analysis showing that no slow-roll inflation occurs in these specific type IIA flux compactifications when all perturbative corrections are included.

## Key findings

- No slow-roll inflation is possible in the studied models.
- The scalar potential exhibits runaway behavior leading to decompactification.
- Inflation cannot be achieved without breaking N=2 supersymmetry.

## Abstract

We investigate whether cosmological inflation is possible in a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, when all perturbative string corrections are taken into account. We confine ourselves to the universal hypermultiplet and an abelian vector multiplet, representing matter in four dimensions. Since all axions can be stabilized by D-instantons, we choose dilaton and a K\"ahler modulus as the only running scalars. Though positivity of their scalar potential can be achieved, we find that there is no slow roll ($\varepsilon > 2$ and $\eta >2$), and no Graceful Exit because the scalar potential has the run-away behaviour resulting in decompactification. We conclude that it is impossible to generate phenomenologically viable inflation in the given class of flux compactifications of type IIA strings, without explicit breaking of $N=2$ local supersymmetry of the low-energy effective action.