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, ϕi , can all be heavier (in absolute value) that the Hubble scale: |mi |/H>1, ∀i.

Inspired by the swampland distance conjecture and the high-slope conjecture, we present two families of multi-field inflationary potentials compatible with the conjectures along the trajectory. One family is a helix-type potential that satisfies the conjectures only locally. This family inflates with V H and produces Planck-compatible scalar perturbations, but a too-high tensor power. Our other family of potentials globally satisfies the swampland conjectures and is in negatively-curved field space. It balances the potential gradient against the geometry to generate high turning rates. Due to the form of the potential, this model has exactly massless entropic perturbations and a light adiabatic mode. In the superhorizon limit, the entropic mode freezes out, which sources linear growth of the adiabatic mode. In contrast to hyperinflation, both families remain under perturbative control.

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.

We study multi-field inflation in random potentials generated via a non-equilibrium random matrix theory process. We make a novel modification of the process to include correlations between the elements of the Hessian and the height of the potential, similar to a Random Gaussian Field (RGF). We present the results of over 50,000 inflationary simulations involving 5-100 fields. For the first time, we present results of O(100) fields using the full 'transport method', without slow-roll approximation. We conclude that Planck compatibility is a common prediction of such models, however significant isocurvature power at the end of inflation is possible.

We investigate the observational signatures of many-field inflation and present analytic expressions for the spectral index as a function of the prior. For a given prior we employ the central limit theorem and the horizon crossing approximation to derive universal predictions, as found previously. However, we also find a specific dependence on the prior choice for initial conditions that has not been seen in previous studies. Our main focus is on quadratic inflation, for which the initial conditions statistics decouple from those of the mass distribution, while other monomials are also briefly discussed. We verify the validity of our calculations by comparing to full numerical simulations with 10 2 fields using the transport method.