${\alpha }^{\prime }$ Inflation: Moduli Stabilisation and Observable Tensors from Higher Derivatives

Abstract

The leading order dynamics of the type IIB Large Volume Scenario is characterised by the interplay between ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$ 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 ${\alpha }^{\prime }$ 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.

arXiv comment21 pages, 3 figures

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