Rapid-turn inflation in supergravity is rare and tachyonic

TL;DR

This paper explores rapid-turn inflation within supergravity frameworks, revealing that large turning rates are possible but require high field space curvature, with stability but tachyonic Hessian eigenvalues, highlighting challenges for string theory models.

Contribution

It demonstrates that rapid-turn inflation can occur in supergravity models with high curvature, and clarifies the absence of the eta-problem in multifield slow-roll inflation.

Findings

Large turning rates are achievable in supergravity models.

Inflationary trajectories are stable despite tachyonic Hessian eigenvalues.

High field space curvature is necessary for rapid-turn inflation.

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 $\eta$-problem in multifield slow-roll inflation and show that it does not arise, inasmuch as the inflatons, $\phi^i$, can all be heavier (in absolute value) that the Hubble scale: $|m_i|/H>1$, $\forall\, i$.