Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations

TL;DR

This paper compares metric and Palatini formalisms in non-minimally coupled inflationary models, revealing differences in predictions and parameter dependencies that impact the inflationary scale and viability.

Contribution

It provides a detailed comparison of metric and Palatini formulations in non-minimal inflation, highlighting their distinct predictions and parameter preferences.

Findings

Palatini prefers larger non-minimal coupling values.

Inflaton remains below Planck scale in Palatini formalism.

Differences in cosmological parameter predictions between formalisms.

Abstract

We analyze non-minimally coupled scalar field theories in metric (second-order) and Palatini (first-order) formalisms in a comparative fashion. After contrasting them in a general setup, we specialize to inflation and find that the two formalisms differ in their predictions for various cosmological parameters. The main reason is that dependencies on the non-minimal coupling parameter are different in the two formalisms. For successful inflation, the Palatini approach prefers a much larger value for the non-minimal coupling parameter than the Metric approach. Unlike the Metric formalism, in Palatini, the inflaton stays well below the Planck scale whereby providing a natural inflationary epoch.