The Multi-Field, Rapid-Turn Inflationary Solution

TL;DR

This paper extends the understanding of rapid-turn multi-field inflation to arbitrary numbers of fields, providing new methods to identify such solutions and applying them to exclude certain inflation scenarios.

Contribution

It generalizes rapid-turn inflation criteria beyond two fields, introduces efficient search methods, and applies these to specific string theory models.

Findings

Efficient methods for finding rapid-turn solutions in multi-field inflation.

Identification of common conditions where the Hessian eigenvector aligns with the gradient.

Exclusion of slow-roll, rapid-turn inflation in a particular potential.

Abstract

There are well-known criteria on the potential and field-space geometry for determining if slow-roll, slow-turn, multi-field inflation is possible. However, even though it has been a topic of much recent interest, slow-roll, rapid-turn inflation only has such criteria in the restriction to two fields. In this work, we generalize the two-field, rapid-turn inflationary attractor to an arbitrary number of fields. We quantify a limit, which we dub extreme turning, in which rapid-turn solutions may be found efficiently and develop methods to do so. In particular, simple results arise when the covariant Hessian of the potential has an eigenvector in close alignment with the gradient -- a situation we find to be common and we prove generic in two-field hyperbolic geometries. We verify our methods on several known rapid-turn models and search two type-IIA constructions for rapid-turn trajectories. For the first time, we are able to efficiently search for these solutions and even exclude slow-roll, rapid-turn inflation from one potential.