The Palatini side of inflationary attractors

TL;DR

This paper investigates how the inflationary attractor behavior in chaotic inflation models with non-minimal coupling is affected when using the Palatini formulation of gravity, revealing that attractors are not universal in this context.

Contribution

It demonstrates that the attractor behavior in non-minimally coupled inflation models does not hold in Palatini gravity, highlighting the dependence on the underlying gravitational theory.

Findings

Attractor behavior is lost in Palatini gravity for these models.

The existence of attractors depends on the gravitational formulation.

Implications for observational predictions of inflation models.

Abstract

We perform an analysis of models of chaotic inflation where the inflaton field $\phi$ is coupled non-minimally to gravity via $\xi \phi^n g^{\mu\nu}R_{\mu\nu}(\Gamma), n>0$. 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.