Pole N-flation

Abstract

A second order pole in the scalar kinetic term can lead to a class of inflation models with universal predictions referred to as pole inflation or $\alpha$-attractors. While this kinetic structure is ubiquitous in supergravity effective field theories, realising a consistent UV complete model in e.g. string theory is a non-trivial task. For one, one expects quantum corrections arising in the vicinity of the pole which may spoil the typical attractor dynamics. As a conservative estimate of the range of validity of supergravity models of pole inflation we employ the weak gravity conjecture (WGC). We find that this constrains the accessible part of the inflationary plateau by limiting the decay constant of the axion partner. For the original single complex field models, the WGC does not even allow the inflaton to reach the inflationary plateau region. We analyze if evoking the assistance of $N$ scalar fields from the open string moduli helps addressing these problems. Pole $N$-flation could improve radiative control by reducing the required range of each individual field. However, the WGC bound prohibiting pole inflation for a single such field persists even for a collective motion of $N$ such scalars if we impose the sublattice WGC. Finally, we outline steps towards an embedding of pole N-flation in type IIB string theory on fibred Calabi-Yau manifolds.