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2018

Attractor Behaviour in Multifield Inflation

Carrilho, Pedro, Mulryne, David, Ronayne, John et al.

Understand

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.