Palatini inflation in models with an $R^2$ term

TL;DR

This paper explores how adding an $R^2$ term in Palatini formalism affects inflationary models with scalar fields, showing it generally lowers the tensor-to-scalar ratio and modifies inflation predictions.

Contribution

It provides a detailed analysis of Palatini inflation models with an $R^2$ term coupled to various scalar fields, including Higgs-like and scale-invariant models, comparing their predictions to observational data.

Findings

$R^2$ term lowers tensor-to-scalar ratio in Palatini inflation.

Modifications to inflationary predictions depend on scalar coupling type.

Models remain consistent with Planck constraints after including $R^2$ term.

Abstract

The Starobinsky model, considered in the framework of the Palatini formalism, in contrast to the metric formulation, does not provide us with a model for inflation, due to the absence of a propagating scalar degree of freedom that can play the role of the inflaton. In the present article we study the Palatini formulation of the Starobinsky model coupled, in general nonminimally, to scalar fields and analyze its inflationary behavior. We consider scalars, minimally or nonminimally coupled to the Starobinsky model, such as a quadratic model, the induced gravity model or the standard Higgs-like inflation model and analyze the corresponding modifications favorable to inflation. In addition we examine the case of a classically scale-invariant model driven by the Coleman-Weinberg mechanism. In the slow-roll approximation, we analyze the inflationary predictions of these models and compare them to the latest constraints from the Planck collaboration. In all cases, we find that the effect of the $R^2$ term is to lower the value of the tensor-to-scalar ratio.