# Scaling attractors in multi-field inflation

## TL;DR

This paper classifies scaling attractors in multi-field inflation with curved scalar geometry, revealing conditions for non-slow-roll behaviour and transitions between different dynamical regimes, enhancing understanding of inflationary dynamics.

## Contribution

It introduces a classification of two-field inflationary scaling solutions, analyzing their stability and role in non-slow-roll, slow-turn inflationary trajectories, including bifurcation phenomena.

## Key findings

- Identification of all scaling solutions as critical points of a dynamical system
- Discovery of bifurcations governing transitions between geodesic and non-geodesic motion
- Reassessment of background stability criteria in multi-field inflation

## Abstract

Multi-field inflation with a curved scalar geometry has been found to support background trajectories that violate the slow-roll, slow-turn conditions and thus have the potential to evade the swampland constraints. In order to understand how generic this novel behaviour is and what conditions lead to it, we perform a classification of dynamical attractors of two-field inflation that are of the scaling type. Scaling solutions form a one-parameter generalization of De Sitter solutions with a constant value of the first Hubble flow parameter $\epsilon$ and, as we argue and demonstrate, form a natural starting point for the study of non-slow-roll slow-turn behaviour. All scaling solutions can be classified as critical points of a specific dynamical system. We recover known multi-field inflationary attractors as approximate scaling solutions and classify their stability using dynamical system techniques. In particular, we discover that dynamical bifurcations play an integral role in the transition between geodesic and non-geodesic motion and discuss the ability of scaling solutions to describe realistic multi-field models. We revisit the criteria for background stability and show cases where the usual criteria found in the literature do not capture the background evolution of the system.