# Attractors, Bifurcations and Curvature in Multi-field Inflation

## TL;DR

This paper unifies various multi-field inflation models through an effective potential framework, analyzing stability, bifurcations, and the role of curvature, and introduces solutions beyond traditional isometry assumptions.

## Contribution

It provides a unified description of multi-field inflation models, including hyperinflation and side-tracked inflation, and explores stability without relying on field-space isometries.

## Key findings

- Hyperinflation is a special case of side-tracked inflation.
- Explicit coordinate transformations relate different inflation models.
- Stable inflationary solutions without field-space isometries are constructed.

## Abstract

Recent years have seen the introduction of various multi-field inflationary scenarios in which the curvature and geodesics of the scalar manifold play a crucial role. We outline a simple description that unifies these different proposals and discuss their stability criteria. We demonstrate how the underlying dynamics is governed by an effective potential, whose critical points and bifurcations determine the late-time behaviour of the system, thus unifying hyperinflation, angular, orbital and side-tracked inflation. Interestingly, we show that hyperinflation is a special case of side-tracked inflation, relying on the enhanced isometries of the hyperbolic manifold. We provide the explicit coordinate transformation that maps the two models into each other. Finally, we relax the assumption of a field-space isometry along the inflationary direction that has been considered a prerequisite in the literature so far. We explicitly construct inflationary solutions that do not proceed along a field-space isometry or geodesic and use them to discuss stability criteria.