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  1. Abstract Strongly non-geodesic, or rapidly turning trajectories in multifield inflation have attracted much interest recently from both theoretical and phenomenological perspectives. Most models with large turning rates in the literature are formulated as effective field theories. In this paper we investigate rapid-turn inflation in supergravity as a first step towards understanding them in string theory. We find that large turning rates can be generated in a wide class of models, at the cost of high field space curvature. In these models, while the inflationary trajectories are stable, one Hessian eigenvalue is always tachyonic and large, in Hubble units. Thus, these models satisfy the de Sitter swampland conjecture along the inflationary trajectory. However, the high curvatures underscore the difficulty of obtaining rapid-turn inflation in realistic string-theoretical models.In passing, we revisit the η -problem in multifield slow-roll inflation and show that it does not arise, inasmuch as the inflatons, ϕ i , can all be heavier (in absolute value) that the Hubble scale: | m i | /H >1, ∀ i . 
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  2. null (Ed.)
    A bstract 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. 
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