Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism

TL;DR

This paper explores a scale-invariant quadratic gravity model in the Palatini formalism, incorporating the Higgs and an extra scalar field, and demonstrates its compatibility with inflationary observations while reducing tensor-to-scalar ratio predictions.

Contribution

It introduces a novel two-field inflationary model within scale-invariant quadratic gravity in the Palatini formalism, analyzing its inflationary predictions and observational viability.

Findings

Model aligns with Planck data across various parameters.

Quadratic curvature terms lower the tensor-to-scalar ratio.

Inflation occurs along a flat direction with a one-loop effective potential.

Abstract

In the framework of classical scale invariance, we consider quadratic gravity in the Palatini formalism and investigate the inflationary predictions of the theory. Our model corresponds to a two-field scalar-tensor theory, that involves the Higgs field and an extra scalar field stemming from a gauge $U(1)_X$ extension of the Standard Model, which contains an extra gauge boson and three right-handed neutrinos. Both scalar fields couple nonminimally to gravity and induce the Planck scale dynamically, once they develop vacuum expectation values. By means of the Gildener-Weinberg approach, we describe the inflationary dynamics in terms of a single scalar degree of freedom along the flat direction of the tree-level potential. The one-loop effective potential in the Einstein frame exhibits plateaus on both sides of the minimum and thus the model can accommodate both small and large field inflation. The inflationary predictions of the model are found to comply with the latest bounds set by the Planck collaboration for a wide range of parameters and the effect of the quadratic in curvature terms is to reduce the value of the tensor-to-scalar ratio.