Inflationary Attractors in $F(R)$ Gravity

Abstract

In this letter we shall demonstrate that the viable $F(R)$ gravities can be classified mainly into two classes of inflationary attractors, either the $R^2$ attractors or the $\alpha$-attractors. To show this, we shall derive the most general relation between the tensor-to-scalar ratio $r$ and the spectral index of primordial curvature perturbations $n_s$, namely the $r-n_s$ relation, by assuming that the slow-roll condition constrains the values of the slow-roll indices. As we show, the relation between the tensor-to-scalar ratio and the spectral index of the primordial curvature perturbations has the form $r\simeq \frac{48(1-n_s{)}^2}{(4-x{)}^2}$, where the dimensionless parameter $x$ contains higher derivatives of the $F(R)$ gravity function with respect to the Ricci scalar, and it is a function of the $e$-foldings number $N$ and may also be a function of the free parameters of the various $F(R)$ gravity models. For $F(R)$ gravities which have a spectral index compatible with the observational data and also yield $x\ll 1$, these belong to the $R^2$-type of attractors, with $r\sim 3(1-n_s{)}^2$, and these are viable theories. Moreover, in the case that $x$ takes larger values in specific ranges and is constant for a given $F(R)$ gravity, the resulting $r-n_s$ relation has the form $r\sim 3\alpha (1-n_s{)}^2$, where $\alpha$ is a constant. Thus we conclude that the viable $F(R)$ gravities may be classified into two limiting types of $r-n_s$ relations, one identical to the $R^2$ model at leading order in $x$, and one similar to the $\alpha$-attractors $r-n_s$ relation, for the $F(R)$ gravity models that yield $x$ constant. Finally, we also discuss the case that $x$ is not constant.

PLB Accepted

References in corpus (12)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Standard Model Higgs boson as the inflaton
• Inflationary Cosmology
• The Unity of Cosmological Attractors
• Cosmology with Nilpotent Superfields
• Single-field $\alpha$-attractors
• Autonomous Dynamical System Approach for $f(R)$ Gravity
• Inflationary $\alpha$-attractors from $F(R)$ Gravity
• Chaotic Inflation in Supergravity after Planck and BICEP2
• Inflation beyond T-models and primordial B-modes
• $\alpha$-Attractors: Planck, LHC and Dark Energy
• Rectifying an Inconsistency in $F(R)$ Gravity Inflation

Cited by in corpus (20)

• Recent Advances on Inflation
• Unifying of Inflation with Early and Late Dark Energy Epochs in Axion $F(R)$ Gravity
• Early Dark Energy with Power-law F(R) Gravity
• $R^p$ Attractors Static Neutron Star Phenomenology
• Enhancement of primordial curvature perturbations in $R^3$-corrected Starobinsky-Higgs inflation
• Universal Inflationary Attractors Implications on Static Neutron Stars
• Inflationary Attractors Predictions for Static Neutron Stars in the Mass-Gap Region
• Kinetic Axion $F(R)$ Gravity Inflation
• Static Neutron Stars Perspective of Quadratic and Induced Inflationary Attractor Scalar-tensor Theories
• Observational constraints on the equation of state of viscous fluid in $f(R,T)$ gravity
• Constraining viscous dark energy equation of state in $f(R,L_m)$ gravity
• Amplification of the Primordial Gravitational Waves Energy Spectrum by a Kinetic Scalar in $F(R)$ Gravity
• Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe
• Cosmic acceleration with bulk viscosity in an anisotropic $f(R,L_m)$ background
• New generalization of the simplest $\alpha$-attractor $T$ model
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• Power law $\alpha$-Starobinsky inflation
• Complementary signatures of $\alpha -$attractor inflation in CMB and cosmic string Gravitational Waves
• Primordial Cosmology of an Emergent-like Universe from Modified Gravity: Reconstruction and Phenomenology Optimization with a Genetic Algorithm
• Cosmological constraints on viable $f(R)$ models using weak lensing