On higher derivative corrections to the $R+R^2$ inflationary model

TL;DR

This paper investigates higher derivative corrections to the $R+R^2$ inflationary model, treating complex terms as small perturbations to avoid ghosts, and explores their observational implications through scalar field mappings.

Contribution

It introduces a perturbative approach to include higher derivative terms like $Rox R$ in the $R+R^2$ model, deriving bounds and comparing with non-perturbative treatments.

Findings

Perturbative treatment yields different observational predictions than full treatment.

An upper bound on the $Rox R$ term coefficient is established.

Mapping to a single scalar field simplifies analysis and reveals key differences.

Abstract

The $R+R^2$ model is successful in describing inflation, as it provides an excellent fit to the full set of available observational data. On the other hand, the same model is the simplest extension of general relativity which does not produce higher derivative ghosts and related instabilities. Long ago, it was proposed to treat all terms which cause higher derivative instabilities as small perturbations that could avoid the presence of ghosts in the spectrum. We put this proposal into practice and consider an explicit example of treating more complicated higher derivative terms as small perturbations over the $R+R^2$ model by introducing the $R\Box R$ term into the action. Within the described scheme, it is possible to obtain an upper bound on the coefficient of this non-scale-free sixth-derivative term by mapping the theory into a one-scalar field potential. It is shown that the result differs from treating this term on equal footing with other terms that requires mapping to a two-scalar field model, and in general leads to different observational consequences.