Second-order corrections to Starobinsky inflation

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.

15 pages plus appendices and references (two-column), 4 figures; v4: In this version that matches to the one accepted by the EPJC, section IV. C. was expanded, new appendix B was added, we made improvements throughout the manuscript and references were added

References in corpus (16)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Black Holes in Higher-Derivative Gravity
• Multiple field inflation
• Static Solutions for 4th order gravity
• On the cancellation of Newtonian singularities in higher-derivative gravity
• Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term
• Reconstruction of Slow-roll $F(R)$ Gravity Inflation from the Observational Indices
• Higher-order extension of Starobinsky inflation: initial conditions, slow-roll regime, and reheating phase
• Cosmology with a light ghost
• Mutated hybrid inflation in $f(R,\square R)$-gravity
• Gravitational waves in higher-order $R^2$ gravity
• Renormalization-group techniques for single-field inflation in primordial cosmology and quantum gravity
• Gravitational waves in massive conformal gravity
• Perturbation Spectra and Renormalization-Group Techniques in Double-Field Inflation and Quantum Gravity Cosmology

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• Higher-order gravity models: corrections up to cubic curvature invariants and inflation
• Inflation in a scalar-vector gravity theory