$\beta$-function reconstruction of Palatini inflationary attractors

TL;DR

This paper uses the $eta$-function formalism to compare inflationary attractors in metric and Palatini gravity, identifying conditions under which they produce indistinguishable observational predictions.

Contribution

It classifies the strong coupling limit of inflationary models in both formalisms and reconstructs potentials to analyze their observational differences.

Findings

Identifies parameter ranges where metric and Palatini models are observationally indistinguishable.

Reconstructs Jordan frame potentials for $\xi$-attractors based on $eta$-function choices.

Demonstrates the impact of metric vs. Palatini formalism on inflationary observables.

Abstract

Attractor inflation is a particularly robust framework for developing inflationary models that are insensitive to the details of the potential. Such models are most often considered in the metric formulation of gravity. However, non-minimal models may not necessarily maintain their attractor nature in the Palatini formalism where the connection is independent of the metric. In this work, we employ the $\beta$-function formalism to classify the strong coupling limit of inflationary models in both the metric and the Palatini approaches. Furthermore, we determine the range of values for the non-minimal coupling that lead to theories being observationally indistinguishable in metric and Palatini within current accuracy. Finally, we reconstruct the Jordan frame potential for $\xi$-attractors by imposing an explicit form for the $\beta$-function, demonstrating the effect that the choice of metric or Palatini has on the inflationary observables of the theory.