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.
Warm natural inflation is studied for the case of the original cosine potential. The radiation bath during inflation induces a dissipation (friction) rate in the equation of motion for the inflaton field, which can potentially reduce the field excursion needed for an observationally viable period of inflation. We examine if the dissipation thus provides a mechanism to avoid the large decay constant f ≳ M pl of cold cosine natural inflation. Whereas temperature independent dissipation has previously been shown to alleviate the need for a trans-Planckian decay constant f, we illustrate here the difficulties of accommodating a significantly sub-Planckian decay constant (f < 10-1 M pl) for the case of a temperature dependent dissipation rate in the form Γ ∝ Tc , with c = {1,3}. Such dissipation rates represent physically well-motivated constructions in the literature. For each model, we map its location in the r-ns plane and compare with cosmic microwave background (CMB) data. For c = 1 (c = 3), we find that agreement with CMB data requires that dissipation be in the weak (moderate) regime and that the minimum allowed value of the decay constant in the potential is f min = 0.3 (0.8) M pl, respectively.
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