$R^2$ Inflation Revisited and Dark Energy Corrections

Abstract

The vacuum $R^2$ model is known to generate a quasi-de Sitter evolution for inflation, using solely the slow-roll assumptions. Using standard reconstruction techniques, we demonstrate that the $f(R)$ gravity which actually realizes the quasi-de Sitter evolution is not simply the $R^2$ model but a deformed $R^2$ model which contains extra terms in addition to the $R^2$ model. We analyze in detail the inflationary dynamics of the deformed $R^2$ model and we demonstrate that the predictions are quite close to the ones of the pure $R^2$ model, regardless the values of the free parameters. Basically the deformed $R^2$ model is also a single parameter inflationary model, exactly like the ordinary $R^2$ model. In contrast to the early-time era, where the deformed $R^2$ model is quite similar to the $R^2$ model, at late times, the phenomenological picture is different. The deformed $R^2$ model describes stronger gravity compared to the ordinary $R^2$ with an effectively smaller effective Planck mass. We propose the addition of an early dark energy term which does not affect at all the inflationary era, but takes over the control of the late-time dynamics at late times. We study in some detail the predicted dark energy era evolution, and we demonstrate that the dark energy corrected deformed $R^2$ model can describe a viable dark energy era, compatible with the Planck constraints on cosmological parameters. Furthermore the model is distinct from the $\Lambda$-Cold-Dark-Matter model, but shows a qualitatively similar behavior.

PRD Accepted

References in corpus (27)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Standard Model Higgs boson as the inflaton
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• The Large Scale Structure of f(R) Gravity
• Constraining f(R) Gravity as a Scalar Tensor Theory
• The Cosmology of Modified Gauss-Bonnet Gravity
• Limit to General Relativity in f(R) theories of gravity
• The Newtonian Limit of F(R) gravity
• Cosmography of f(R) gravity
• Stability of Cosmological Solution in f(R) Models of Gravity
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• The evolution of density perturbations in f(R) gravity
• Junction Conditions in f(R) Theories of Gravity
• Sensitivity to a Frequency-Dependent Circular Polarization in an Isotropic Stochastic Gravitational Wave Background
• Unifying of Inflation with Early and Late Dark Energy Epochs in Axion $F(R)$ Gravity
• Aspects of cosmological expansion in F(R) gravity models
• Gauss-Bonnet cosmologies: crossing the phantom divide and the transition from matter dominance to dark energy
• Unification of Inflation with Dark Energy in $f(R)$ Gravity and Axion Dark Matter
• Geometric Inflation and Dark Energy with Axion $F(R)$ Gravity
• $f(R)$ Gravity Inflation with String-Corrected Axion Dark Matter
• Observational constraints on slow-roll inflation coupled to a Gauss-Bonnet term
• A Refined Einstein-Gauss-Bonnet Inflationary Theoretical Framework
• Cosmic history of viable exponential gravity: Equation of state oscillations and growth index from inflation to dark energy era
• Unification of a Bounce with a Viable Dark Energy Era in Gauss-Bonnet Gravity

Cited by in corpus (12)

• Enhancement of primordial curvature perturbations in $R^3$-corrected Starobinsky-Higgs inflation
• Observational Constraints on Dark Energy Models with $\Lambda$ as an Equilibrium Point
• Running of the Spectral Index and Inflationary Dynamics of $F(R)$ Gravity
• Effects of a Pre-inflationary de Sitter Bounce on the Primordial Gravitational Waves in $f(R)$ Gravity Theories
• Testing scale-invariant inflation against cosmological data
• Renyi Holographic Dark Energy models in Teleparallel gravity
• Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory
• Towards a unified interpretation of the early Universe in $R^2$-corrected dark energy model of $F(R)$ gravity
• Cosmological application of the Maxwell gravity
• Self-tuning inflation
• A connection between Gravitational Scalar-Tensor theories and Generalized Hybrid theories
• On inflationary parameters in scalar-tensor theories