Special Points of Inflation in Flux Compactifications

TL;DR

This paper explores how axion inflation models can be realized in the complex structure moduli spaces of Calabi-Yau manifolds, identifying special points with monodromy symmetries that enable various inflationary potentials.

Contribution

It demonstrates the realization of axion inflation near special points in moduli spaces, introducing new geometric scenarios and potential forms in flux compactifications.

Findings

Identification of special points with monodromy symmetries in moduli spaces.

Construction of toy models for natural and axion monodromy inflation.

Examples involving mirror geometries with Mordell-Weil groups.

Abstract

We study the realisation of axion inflation models in the complex structure moduli spaces of Calabi-Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure point and conifold point, but can be of more general nature. In Type IIB and F-theory compactifications the geometric axions receive a scalar potential from a flux-induced superpotential. We find toy variants of various inflationary potentials including the ones for natural inflation of one or multiple axions, or axion monodromy inflation with polynomial potential. Interesting examples are also given by mirror geometries of torus fibrations with Mordell-Weil group of rank $N-1$ or an $N$-section, which admit an axion if $N>3$.