On the Consistency of Rapid-Turn Inflation

TL;DR

This paper demonstrates that the consistency conditions in two-field rapid-turn inflation models inherently support the regime's longevity, extending previous understanding of its sustainability for multiple e-folds.

Contribution

It proves that the consistency conditions ensure the persistence of rapid-turn inflation, even under the most general definitions, and includes a class of models with large turn rates.

Findings

Consistency conditions guarantee rapid-turn inflation longevity.

Generalized conditions apply to a broad class of models.

Certain models maintain large turn rates even when not large.

Abstract

Recent studies, in the context of consistency conditions for rapid-turn and third order slow-roll inflation in two-field models, raised the question whether this regime can be sustained for more than a few e-folds of expansion. We answer this question in the affirmative by showing that the consistency conditions themselves ensure the longevity of the rapid-turn regime. Furthermore, we prove this for the most general definition of rapid turning (i.e., with a turning rate that is large compared to the slow-roll parameters, but not necessarily large compared to unity), using in the process a generalized consistency condition. We also show that a special class of rapid-turn models, including angular inflation, satisfy a large-(compared to $1$)-turn-rate condition even for non-large turning rates.