Second-order corrections to Starobinsky inflation

• Published in: The European physical journal. C, Particles and fields Vol. 83; no. 11; pp. 1032 - 19
• Main Authors: Rodrigues-da-Silva, G., Medeiros, L. G.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-11-2023; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Astronomy; Astrophysics and Cosmology; Curvature; Elementary Particles; Gravitational waves; Gravity; Hadrons; Heavy Ions; High energy physics; Hypotheses; Inflation (cosmology); Inflation (Finance); Investigations; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Perturbation; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Relativity; Spacetime; String Theory; Theory of relativity
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-023-12149-8

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
□
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.