Second-order corrections to Starobinsky inflation

TL;DR

This paper explores second-order curvature corrections in extended gravity theories to model inflation, analyzing phase space, perturbations, and comparing predictions with recent cosmological observations.

Contribution

It introduces a second-order corrected gravity model for inflation, including $R^2$, $R^3$, and $R\square R$ terms, and studies its cosmological implications.

Findings

Model successfully describes inflationary dynamics.

Perturbation evolution aligns with observational data.

Confronts model with Planck, BICEP3/Keck, and BAO results.

Abstract

Higher-order theories of gravity are extensions to general relativity (GR) motivated mainly by high-energy physics searching for GR ultraviolet completeness. They are characterized by the inclusion of correction terms in the Einstein-Hilbert action that leads to higher-order field equations. In this paper, we propose investigating inflation due to the GR extension built with all correction terms up to the second-order involving only the scalar curvature $R$, namely, $R^{2}$, $R^{3}$, $R\square R$. We investigate inflation within the Friedmann cosmological background, where we study the phase space of the model, as well as explore inflation in slow-roll leading-order. Furthermore, we describe the evolution of scalar perturbations and properly establish the curvature perturbation. Finally, we confront the proposed model with recent observations from Planck, BICEP3/Keck, and BAO data.