$\alpha'$ Inflation: Moduli Stabilisation and Observable Tensors from Higher Derivatives

TL;DR

This paper demonstrates how higher derivative $'$ corrections can lift flat directions in type IIB string compactifications, enabling inflation with observable tensor modes consistent with current cosmological data.

Contribution

It introduces a mechanism where $'$ corrections stabilize flat directions in Calabi-Yau compactifications, leading to viable inflation models with detectable gravitational waves.

Findings

Flat directions can be lifted by higher derivative $'$ corrections.

Inflationary models predict a tensor-to-scalar ratio around 0.01.

Spectral index aligns with observational data.

Abstract

The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between $\alpha'$ and non-perturbative effects which fix the overall volume and all local blow-up modes leaving (in general) several flat directions. In this paper we show that, in an arbitrary Calabi-Yau with at least one blow-up mode resolving a point-like singularity, any remaining flat directions can be lifted at subleading order by the inclusions of higher derivative $\alpha'$ corrections. We then focus on simple fibred cases with one remaining flat direction which can behave as an inflaton if its potential is generated by both higher derivative $\alpha'$ and winding loop corrections. Natural values of the underlying parameters give a spectral index in agreement with observational data and a tensor-to-scalar ratio of order $r=0.01$ which could be observed by forthcoming CMB experiments. Dangerous corrections from higher dimensional operators are suppressed due to the presence of an approximate non-compact shift symmetry.