Attractor Behaviour in Multifield Inflation

TL;DR

This paper investigates how non-minimal couplings in multifield inflation models influence inflationary dynamics, revealing that gravity formulation determines whether multifield models behave like single-field models at large couplings.

Contribution

It demonstrates that in large coupling regimes, the Einstein frame field-space curvature does not affect inflationary dynamics, with the gravity formulation dictating whether multifield models exhibit attractor behavior.

Findings

In the metric case, multifield models approach single-field $ ext{alpha}$-attractor behavior.

In the Palatini case, attractor behavior is absent even at large couplings.

Gravity formulation critically influences the inflationary attractor properties.

Abstract

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.