The Palatini side of inflationary attractors

Abstract

We perform an analysis of models of chaotic inflation where the inflaton field $\varphi$ is coupled non-minimally to gravity via $\xi {\varphi }^n{g}^{\mu \nu }{R}_{\mu \nu }(\Gamma ),n>0$. We focus on the Palatini theory of gravity, i.e. the case where the assumptions of the General Relativity are relaxed (that of the connection being the Levi-Civita one) and the gravitational degrees of freedom are encoded not only in the metric but also the connection $\Gamma$, which is treated as an independent variable. We show that in this case the famous attractor behaviour of simple non-minimally coupled models of inflation is lost. Therefore the attractors are not universal but their existence depends on the underlying theory of gravity in a subtle way. We discuss what this means for chaotic models and their observational consequences.

5 pages, 1 figure. v2: Notation clarified, references and discussion added

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