$k$-essence $f(R)$ Gravity Inflation

Abstract

In this work we study a modified version of $f(R)$ gravity in which higher order kinetic terms of a scalar field are added in the action of vacuum $f(R)$ gravity. This type of theory is a type of $k$-essence $f(R)$ gravity, and it belongs to the general class of $f(R,\varphi ,X)$ theories of gravity, where $\varphi$ is a scalar field and $X=\frac{1}{2}{\partial }^{\mu }\varphi {\partial }_{\mu }\varphi$. We focus on the inflationary phenomenology of the model, in the slow-roll approximation, and we investigate whether viable inflationary evolutions can be realized in the context of this theory. We use two approaches, firstly by imposing the slow-roll conditions and by using a non-viable vacuum $f(R)$ gravity. As we demonstrate, the spectral index of the primordial scalar perturbations and the tensor-to-scalar ratio of the resulting theory can be compatible with the latest observational data. In the second approach, we fix the functional form of the Hubble rate as a function of the $e$-foldings number, and we modify well-known vacuum $f(R)$ gravity reconstruction techniques, in order to find the $k$-essence $f(R)$ gravity which can realize the given Hubble rate. Accordingly, we calculate the slow-roll indices and the corresponding observational indices, and we also provide general formulas of these quantities in the slow-roll approximation. As we demonstrate, viability can be obtained in this case too, however the result is strongly model dependent. In addition, we discuss when ghosts can occur in the theory, and we investigate under which conditions ghosts can be avoided by using a particular class of models. Finally, we qualitatively discuss the existence of inflationary attractors for the non-slow-roll theory, and we provide hints towards finding general de Sitter attractors for the theory at hand.

arXiv commentNPB Accepted

References in corpus (49)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• Essentials of k-essence
• f(T) teleparallel gravity and cosmology
• Kinetically Driven Quintessence
• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• From k-essence to generalised Galileons
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• BICEP2 / Keck Array VI: Improved Constraints On Cosmology and Foregrounds When Adding 95 GHz Data From Keck Array
• Purely kinetic k-essence as unified dark matter
• Matter Bounce Cosmology with the f(T) Gravity
• k-Essence, superluminal propagation, causality and emergent geometry
• Towards a Nonsingular Bouncing Cosmology
• Bouncing Cosmologies: Progress and Problems
• Cosmological reconstruction of realistic modified F(R) gravities
• Extended tachyon field, Chaplygin gas and solvable k-essence cosmologies
• Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modified gravity theories
• Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyon: Unified analyses
• Tracking K-essence
• Exploring Bouncing Cosmologies with Cosmological Surveys
• Multifield Inflation after Planck: The Case for Nonminimal Couplings
• A new view of k-essence
• Dynamics of $k$-essence
• Kinetic k-essence and Quintessence
• Haloes of k-Essence
• Cosmological perturbations in a generalized gravity including tachyonic condensation
• On causality and superluminal behavior in classical field theories. Applications to k-essence theories and MOND-like theories of gravity
• Phantom Inflation and Primordial Perturbation Spectrum
• Power-law expansion in k-essence cosmology
• Autonomous Dynamical System Approach for $f(R)$ Gravity
• K-essence and the coincidence problem
• Phantom k-essence cosmologies
• Inflationary spectra in generalized gravity: Unified forms
• An Extended Matter Bounce Scenario: current status and challenges
• On the Stability of Phantom K-essence Theories
• On $R+\alpha R^2$ Loop Quantum Cosmology
• Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data
• Autonomous Dynamical System Approach for Inflationary Gauss-Bonnet Modified Gravity
• Cyclic Universe with Quintom matter in Loop Quantum Cosmology
• Reconstruction of k-essence model
• Phantom Inflation in Little Rip
• Loop Quantum Cosmology Corrected Gauss-Bonnet Singular Cosmology
• Phantom Inflation with A Steplike Potential
• Loop Quantum Cosmology Scalar Field Models
• Qualitative study in Loop Quantum Cosmology

Cited by in corpus (24)

• Anisotropic compact stars in $f(R)$ gravity
• Validation of Energy Conditions in Wormhole Geometry within Viable $f(R)$ Gravity
• Traversable wormholes in $f(R)$ gravity with constant and variable redshift functions
• Non-trivial black hole solutions in $f(R)$ gravitational theory
• Static Traversable Wormholes in $f(R,T)=R+2\alpha \ln T$ Gravity
• Estimation of Cosmological Parameters, Stability Analysis and Energy Conditions in Viable Modified Gravity
• Exact theory for the Rezzolla-Zhidenko metric and self-consistent calculation of quasinormal modes
• The key role of Lagrangian multiplier in mimetic gravitational theory in the frame of isotropic compact star
• New rotating AdS/dS black holes in $\mathrm{f}(\mathrm{R})$ gravity
• The Phase Space of $k$-Essence $f(R)$ Gravity Theory
• Testing scale-invariant inflation against cosmological data
• Collapsing scenario for the k-essence emergent generalised Vaidya spacetime in the context of massive gravity's rainbow
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Wormhole modeling in $R^2$ gravity with linear trace term
• Reheating constraints on K-inflation
• Constraints on the speed of sound in the k-essence model of dark energy
• $f(\bar{R},L(X))$-gravity in the context of dark energy with power law expansion and energy conditions
• Alternative approach to the Starobinsky model for inflation scenarios
• Dark energy with a shift-symmetric scalar field: obstacles, loophole hunting and dead ends
• Inflation with exotic kinetic terms in Einstein-Chern-Simons gravity
• An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field
• A study on causality in $f(R,\varphi ,X)$ theory
• The K-essence flow seen from the preferred frame $S_V$. A scalar field theory with Landau superfluid structure
• K-nonizing