Attractor behaviour in multifield inflation

We study multifield inflation in scenarios where the fields are coupled non-minimally to gravity via xi(I)(phi(I))(n)g(mu nu)R(mu nu), where xi(I) are coupling constants, phi(I) the fields driving inflation, g(mu nu) the space-time metric, R-mu nu the Ricci tensor, and n > 0. We consider the so-called alpha-attractor models in two formulations of gravity: in the usual metric case where R-mu nu=R-mu nu(g(mu nu)), and in the Palatini formulation where R-mu nu is an independent variable. As the main result, we show that, regardless of the underlying theory of gravity, the field-space curvature in the Einstein frame has no influence on the inflationary dynamics at the limit of large xi(I), and one effectively retains the single-field case. However, the gravity formulation does play an important role: in the metric case the result means that multifield models approach the single-field alpha-attractor limit, whereas in the Palatini case the attractor behaviour is lost also in the case of multifield inflation. We discuss what this means for distinguishing between different models of inflation.