Higher-order modified Starobinsky inflation

TL;DR

This paper extends the Starobinsky inflation model by adding a derivative term of the scalar curvature, analyzing its implications for inflation, perturbations, and compatibility with recent observations, showing an increased tensor-to-scalar ratio.

Contribution

It introduces a novel extension of the Starobinsky model with a derivative curvature term and analyzes its inflationary dynamics and observational predictions.

Findings

Inflation is achievable with the extended model.

The tensor-to-scalar ratio can be up to three times higher.

The model's predictions are compared with BICEP2/Keck data.

Abstract

An extension of the Starobinsky model is proposed. Besides the usual Starobinsky Lagrangian, a term proportional to the derivative of the scalar curvature, $\nabla_{\mu}R\nabla^{\mu}R$, is considered. The analyzis is done in the Einstein frame with the introduction of a scalar field and a vector field. We show that inflation is attainable in our model, allowing for a graceful exit. We also build the cosmological perturbations and obtain the leading-order curvature power spectrum, scalar and tensor tilts and tensor-to-scalar ratio. The tensor and curvature power spectrums are compared to the most recent observations from BICEP2/Keck collaboration. We verify that the scalar-to-tensor rate $r$ can be expected to be up to three times the values predicted by Starobinsky model.