Ultraviolet Unitarity Violations in Non-minimally Coupled Scalar-Starobinsky Inflation

TL;DR

This paper investigates the energy scales at which scalar-$R^2$ inflation models violate unitarity in the ultraviolet regime, considering different formulations and inflation scenarios to ensure theoretical consistency.

Contribution

It introduces an analysis of UV unitarity violation scales in scalar-$R^2$ inflation models with additional terms, comparing metric and Palatini formulations and applying to known inflation potentials.

Findings

Identifies conditions for unitarity preservation up to the Planck scale.

Analyzes scattering amplitude behavior during inflation and reheating.

Provides parameter ranges ensuring model consistency.

Abstract

We perform the calculation for tree-level ultraviolet unitarity violation scales for scalar-$R^2$ inflation models by including an additional $R^2 |\Phi|^2$-type term. Due to certain constraints, we resort to the Einstein frame for our calculations, where we separate our analysis between metric and Palatini formulations. We follow recent works in this line that debunk the naive predictions for unitarity violations in Higgs' inflation models to determine how to accurately estimate the behaviour of scattering amplitudes in the UV limit. Later, we work out different cases by assuming potentials corresponding to known inflation scenarios so we could predict the range of coupling parameters for which the theories would remain unitary up to the Planckian regime. We also try to find the behaviour of the scattering amplitudes for these theories during the transition from inflationary to reheating epoch.