(Slow-)Twisting inflationary attractors

Abstract

We explore in detail the dynamics of multi-field inflationary models. We first revisit the two-field case and rederive the coordinate independent expression for the attractor solution with either small or large turn rate, emphasizing the role of isometries for the existence of rapid-turn solutions. Then, for three fields in the slow-twist regime we provide elegant expressions for the attractor solution for generic field-space geometries and potentials and study the behaviour of first order perturbations. For generic $\mathcal{N}$-field models, our method quickly grows in algebraic complexity. We observe that field-space isometries are common in the literature and are able to obtain the attractor solutions and deduce stability for some isometry classes of $\mathcal{N}$-field models. Finally, we apply our discussion to concrete supergravity models. These analyses conclusively demonstrate the existence of $\mathcal{N}>2$ dynamical attractors distinct from the two-field case, and provide tools useful for future studies of their phenomenology in the cosmic microwave background and stochastic gravitational wave spectrum.