Attractors, Bifurcations and Curvature in Multi-field Inflation

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.