Exponential Inflation with $F(R)$ Gravity

Abstract

In this paper we shall consider an exponential inflationary model in the context of vacuum $F(R)$ gravity. By using well-known reconstruction techniques, we shall investigate which $F(R)$ gravity can realize the exponential inflation scenario at leading order in terms of the scalar curvature, and we shall calculate the slow-roll indices and the corresponding observational indices, in the context of slow-roll inflation. We also provide some general formulas of the slow-roll and the corresponding observational indices in terms of the $e$-foldings number. In addition, for the calculation of the slow-roll and of the observational indices, we shall consider quite general formulas for which the assumption that all the slow-roll indices are much smaller than unity, is not necessary to hold true. Finally, we investigate the phenomenological viability of the model by comparing it with the latest Planck and BICEP2/Keck-Array observational data. As we demonstrate, the model is compatible with the current observational data for a wide range of the free parameters of the model.

arXiv commentPRD Accepted

References in corpus (52)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• f(T) teleparallel gravity and cosmology
• Modified teleparallel gravity: inflation without inflaton
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Universality Class in Conformal Inflation
• Formalising the Slow-Roll Approximation in Inflation
• Superconformal Inflationary $\alpha$-Attractors
• BICEP2 / Keck Array VI: Improved Constraints On Cosmology and Foregrounds When Adding 95 GHz Data From Keck Array
• Unifying inflation with LambdaCDM epoch in modified f(R) gravity consistent with Solar System tests
• Matter Bounce Cosmology with the f(T) Gravity
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Finite-time future singularities in modified Gauss-Bonnet and $\mathcal{F}(R,G)$ gravity and singularity avoidance
• Minimal Supergravity Models of Inflation
• Bouncing Cosmologies: Progress and Problems
• Ekpyrotic and Cyclic Cosmology
• Cosmological reconstruction of realistic modified F(R) gravities
• A Critical Review of Classical Bouncing Cosmologies
• Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modified gravity theories
• Exploring Bouncing Cosmologies with Cosmological Surveys
• Bouncing cosmology in modified Gauss-Bonnet gravity
• Singular Bouncing Cosmology from Gauss-Bonnet Modified Gravity
• Nearly Starobinsky inflation from modified gravity
• Inflationary universe from perfect fluid and $F(R)$ gravity and its comparison with observational data
• Models for Little Rip Dark Energy
• A polynomial f(R) inflation model
• f(R) gravity theory and CMBR constraints
• Bouncing cosmology with future singularity from modified gravity
• Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
• Further Exact Cosmological Solutions to Higher-Order Gravity Theories
• Singular Inflationary Universe from $F(R)$ Gravity
• Inflationary spectra in generalized gravity: Unified forms
• F(R) gravity and inflation
• Bouncing cosmologies with dark matter and dark energy
• Inflationary $\alpha$-attractors from $F(R)$ Gravity
• An Extended Matter Bounce Scenario: current status and challenges
• Unified Analysis of Cosmological Perturbations in Generalized Gravity
• Cosmic Bounces and Cyclic Universes
• Trace-anomaly driven inflation in modified gravity and the BICEP2 result
• Solving higher curvature gravity theories
• Higher-order gravity and the cosmological background of gravitational waves
• Inflation and dark energy from f(R) gravity
• Precision Predictions for the Primordial Power Spectra from f(R) Models of Inflation
• Constraints on Singular Evolution from Gravitational Baryogenesis
• Singular $F(R)$ Cosmology Unifying Early and Late-time Acceleration with Matter and Radiation Domination Era
• Phantom Inflation in Little Rip
• Inverse Symmetric Inflationary Attractors
• Bouncing Cosmologies

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• Intermediate Coupling Regime in Dilatonic $f(R,T)$ Inflationary Universe
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