Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion

Abstract

A general approach to viable modified $f(R)$ gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with care. Special focus is made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models are explicitly considered, but the analysis is extensible to $N$-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way. Moreover, it is demonstrated that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom.

arXiv comment15 pages, 2 figures, version to appear in Physical Review D

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• Analytic Electrically Charged Black Holes in $F(R)$-ModMax Theory
• Modified gravity with an exponential function of curvature
• Noether Symmetries and Anisotropic Universe in Energy-Momentum Squared Gravity
• Late Time Cosmological Evolution in f(R) theories with Ordinary and Collisional Matter
• Einstein-Yang-Mills AdS Black Brane Solution in Massive Gravity and Viscosity Bound
• Cosmological evolution with quadratic gravity and nonideal fluids
• Simulation of geodesic trajectory of charged BTZ black holes in massive gravity
• The post-Minkowskian limit of f(R)-gravity
• Stability and Space Phase Analysis in f(R) theory with Generalized Exponential model
• Nonminimal coupling inflation with constant slow roll
• Specific neutral and charged black holes in $f(R)$ gravitational theory
• Solar System tests of some models of modified gravity proposed to explain galactic rotation curves without dark matter
• Vacuum Solution of a Linear Red-Shift Based Correction in $f(R)$ Gravity
• Late-time acceleration and inflation in a Poincaré gauge cosmological model
• Modified Gauss-Bonnet Gravity with Radiating Fluids
• Equation of State of Neutron Stars with Junction Conditions in the Starobinsky Model
• Wormhole Geometries Supported by Strange Quark Matter and Phantom-like Generalized Chaplygin gas within $f(Q)$ Gravity
• Scalar field localization on deformed extra space
• Analytic Solutions and Observational support: A study of $f(R,T)$ gravity with $f(R,T)=R+h(T)$
• $f(T)$ non-linear massive gravity and the cosmic acceleration
• Temperature in warm inflation in non minimal kinetic coupling model
• Superpotential method for $F(R)$ cosmological models
• Cosmological Consequences of Exponential Gravity in Palatini Formalism
• Non-Minimal Warm Inflation and Perturbations on the Warped DGP Brane with Modified Induced Gravity
• Implications of the Holst term in a $f(R)$ theory with torsion
• Revisiting compact star in $F(R)$ gravity: Roles of chameleon potential and energy conditions
• Invisibility of antisymmetric tensor fields in the light of $F(R)$ gravity
• Cosmological model with linear equation of state parameter in f(R, Lm) gravity
• Uniqueness of non-trivial spherically symmetric black hole solution in special classes of F(R) gravitational theory
• Linear perturbations in viable f(R) theories
• Quasi-normal Modes of Static Spherically Symmetric Black Holes in $f(R)$ Theory
• Generalized Uncertainty Principle and Black Holes in Higher Dimensional Self-Complete Gravity
• Dynamically Generated Inflation from Non-Riemannian Volume Forms
• Observational signatures of a static $f(R)$ black hole with thin accretion disk
• Constraint propagation equations of the 3+1 decomposition of f(R) gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• The Scale Factor Potential Approach to Inflation
• Curvaton reheating in a Scale Invariant Two Measures Theory
• Friedmann equations in the Codazzi parametrization of Cotton and extended theories of gravity and the Dark Sector
• Topological phantom AdS black holes in $F(R)$ gravity
• Further Refining Swampland dS Conjecture in Mimetic f(G) Gravity
• Testing f(R)-gravity models with DESI DR2 2025-BAO and other cosmological data
• Rescaled Einstein-Hilbert Gravity: Inflation and the Swampland Criteria
• Supernova, baryon acoustic oscillations, and CMB surface distance constraints on f(G) higher order gravity models
• Black Holes with Electric and Magnetic Charges in $F(R)$ Gravity
• On Shapiro time delay in massive scalar-tensor theories
• Non-Minimal Braneworld Inflation after the Planck
• A Study of Black Holes in $F(R)-$ModMax Gravity: Gravitational Lensing and Constraints from EHT Observations
• Graviton and scalar propagations on AdS(4) space in f(R) gravities
• Withholding Potentials, Absence of Ghosts and Relationship between Minimal Dilatonic Gravity and f(R) Theories
• Inflation and late-time accelerated expansion driven by $k$-essence degenerate dynamics
• Dynamically Generated Inflationary Lambda-CDM
• Evolution of Spherical Overdensities in Energy-Momentum-Squared Gravity
• Looking for empty topological wormhole spacetimes in $F(R)$-modified gravity
• A new approach to cosmological perturbations in f(R) models
• An analytic calculation of the growth index for $f(R)$ dark energy model
• Early evolution of fully convective stars in scalar-tensor gravity
• Topological electro-vacuum solutions in extended gravity
• f(T) Quantum Cosmology
• Thin accretion disk signatures in hybrid metric-Palatini gravity
• $f(Q,T)$ gravity: From early to late-time cosmic acceleration
• Equilibrium configuration of perfect fluid orbiting around black holes in some classes of alternative gravity theories
• Fractional Einstein-Gauss-Bonnet scalar field cosmology
• Finite-time singularities in modified $\mathcal{F}(R,G)$-gravity and singularity avoidance
• Cosmological constraints on $\gamma$-gravity models
• Cosmic acceleration and phantom crossing in $f(T)$-gravity
• Two-dimensional Lifshitz-like AdS black holes in $F(R)$ gravity
• A generalized $\Lambda$CDM model with parameterized Hubble parameter in particle creation, viscous and $f(R)$ model framework
• The study of Kantowski-Sachs perfect fluid cosmological model in modified gravity
• Swampland Criteria and Constraints on Inflation in a $f(R,T)$ Gravity Theory
• F(R) cosmology via Noether symmetry and lambda-Chaplygin Gas like model
• Viscous Accelerating Universe with Non-linear and Logarithmic Equation of State Fluid
• Cosmological back-reaction in modified gravity and its implications for dark energy
• First law of thermodynamics and entropy of FLRW universe in modified gravity
• Black Holes and Wormholes Beyond Classical General Relativity
• Cooling process of substellar objects in scalar-tensor gravity
• Singular inflation from Born-Infeld-f(R) gravity
• Bohmian Quantization of the Big Rip
• Late-time Cosmology of scalar field assisted $f(\mathcal{G})$ gravity
• Gravitational waves in Modified Gauss-Bonnet Gravity
• Interpenetrating subspaces as a funnel to extra space
• An extension of the cosmological standard model with a bounded Hubble expansion rate
• New black hole solutions in three-dimensional $f(R)$ gravity
• Relativistic stars in Starobinsky gravity with the matched asymptotic expansions method
• Gravity and Matters on a pure geometric thick polynomial $f(R)$ brane
• Reconstruction of the singularity-free $f(\mathcal{R})$ gravity via Raychaudhuri equations
• Gravitational radiation from binary systems in $f(R)$ gravity: A semi-classical approach
• Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory
• Spherically symmetric and static solutions in $f(R)$ gravity coupled with EM fields
• Bouncing cosmological models in a functional form of F(R) gravity
• Covariant gauge invariant theory of Scalar Perturbations in $f(R)$-gravity: a brief review
• Kinetic Axion Dark Matter in String Corrected $f(R)$ Gravity
• Universal procedure to cure future singularities of dark energy models
• Consistency of Cubic Galileon Cosmology: Model-Independent Bounds from Background Expansion and Perturbative Analyses
• Reconstruction of f(R) gravity models from observations
• Anisotropic Born-Infeld-f(R) Cosmologies
• $R^2$ Gravity Effects on the Kinetic Axion Phase Space
• Constraints on a $f(R)$ gravity dark energy model with early scaling evolution
• New Wormhole Solutions in a Viable $f(R)$ Gravity Model
• $\gamma$ gravity: Steepness control
• Cosmological evolutions in Tsujikawa model of $f(R)$ Gravity
• Towards an optimal marked correlation function analysis for the detection of modified gravity
• Analysis of the cosmological evolution parameters, energy conditions, and linear matter perturbations of an exponential-type model in $f(Q)$ gravity
• Are we seeing the beginnings of Inflation?
• Analysis cosmological tachyon and fermion model and observation data constraints
• Cosmological dynamics of fourth order gravity
• A Note on de Sitter Embedding of $f(R)$ Theories
• De Sitter and power-law solutions in some models of modified gravity
• Impact of Non-metricity and Matter Source on the Geometry of Anisotropic Spheres
• Lower tensor-to-scalar ratio as possible signature of modified gravity
• The phase transition of Rastall AdS black hole with cloud of strings and quintessence
• Dynamics of dwarf galaxies in $f(R)$ gravity
• Reconstructing modified gravity with holographic vacuum energy density
• Cosmological production of black holes: a way to constrain alternative theories of gravity
• N-body Simulations of $\gamma$ Gravity
• Constraints on the Combined Models with $R^{2-q}$ Inflation and Viable $f(R)$ Dark Energy
• A new $F(R)$-gravity model
• Spatially Homogeneous Rotating Solution in f(R) Gravity and Its Energy Contents
• A minimal set of invariants as a systematic approach to higher order gravity models: Physical and Cosmological Constraints
• Qualitative evolution in f(R) cosmologies
• Singularity problem in f(R) model with non-minimal coupling
• A reconstruction method for anisotropic universes in unimodular $F(R)$-gravity
• A Phase Space Diagram for Gravity
• Phantom Divide Crossing with General Non-minimal Kinetic Coupling
• Cosmological constraints on $R^2$-corrected Appleby-Battye model
• Phase-space analysis of torsion-coupled dilatonic ghost condensate
• Non-linear logarithmic interactions and a varying polytropic gas
• Unification of the inflation with late-time acceleration in Born-Infeld-$f(R)$ gravity
• Future cosmological evolution in $f(R)$ gravity using two equations of state parameters
• Exploring the viability of charged Spheres admitting non-metricity and matter source
• The Galaxy Halo Connection in Modified Gravity Cosmologies: Environment Dependence of Galaxy Luminosity function
• Local gravity test of unified models of inflation and dark energy in $f(R)$ gravity
• The non-Abelian Weyl-Yang-Kaluza-Klein gravity model
• Dynamical stability of Minkowski space in higher order gravity
• Reconstruction of $f(R)$ lagrangian from a massive scalar field
• Inflation in non-local hybrid metric-Palatini gravity
• A review of the stochastic background of gravitational waves in f(R) gravity with WMAP constrains
• Pure geometric $f(R)$ branes
• High frequency limit for gravitational perturbations of cosmological models in modified gravity theories
• Non-linear density-velocity dynamics in $f(R)$ gravity from spherical collapse
• A New Exponential Gravity
• de Sitter field equations from quadratic curvature gravity: A group theoretical approach
• Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate
• Cosmology of Horava-Lifshitz f(R) Gravity
• Viability of Arctan Model of f(R) Gravity for Late-time Cosmology
• Superconducting Cosmic Strings and One Dimensional Extended Supersymmetric Algebras
• From inflation to dark energy in scalar-tensor cosmology
• Modified gravity with disappearing cosmological constant
• Einstein Spaces Modeling Nonminimal Modified Gravity
• Trans-Planckian Effect in $f(R)$ Cosmology
• Perturbations of quasi-Newtonian universes in scalar-tensor gravity
• Phantom Mimicry on the Normal Branch of a DGP-inspired Braneworld Scenario with Curvature Effect
• Viability of general relativity and modified gravity cosmologies using high-redshift cosmic probes
• Generalized modified gravity models: the stability issue
• Constraints on dark energy evolution
• Magnetic Suppression of Cosmic Rays' Flux in $\mathbf{f}(\mathbf{R})$ and $\mathbf{f}(\mathbf{Q})$ Theories of Gravity
• Cosmology in a model with Lagrange multiplier, and Gauss-Bonnet and non-minimal kinetic couplings
• Behavior of $F(R)$ gravity around a crossing of the phantom divide
• Shadow of F(R)-EH Black Hole and Constraints from EHT Observations
• The shadow of black holes in $F(R)$-ModMax theory with cosmic strings
• Growth of matter perturbations for realistic $F(R)$ models
• Cosmic acceleration in asymptotically Ricci flat Universe
• "All that matter ... in one Big Bang ...," & other cosmological singularities
• Inflation constraints for classes of f(R) models
• Born - Infeld-type modified gravity
• Cosmological Inflation in a Generalized Unimodular Gravity
• A new model of arcsin-gravity
• The Impact of $f(\mathcal{G},T)$ Gravity on the Evolution of Cavity in the Cluster of Stars
• Dynamical Systems Analysis of $f(R,L_m)$ Gravity Model
• Screening fifth forces in scalar-vector-tensor theories
• Construction of f(R) Gravity Models
• Localized Fermions on Superconducting Domain Walls and Extended Supersymmetry with non-trivial Topological Charges
• Resembling holographic dark energy with f(R)gravity as scalar field and ghost dark energy with tachyon scalar fields
• Toy models of Universe with an Effective varying $\Lambda$-Term in Lyra Manifold
• A New f(R) Model in the Light of Local Gravity Test and Late-time Cosmology
• Modified Gravity in the framework of holographic dark energy
• Exact charged black hole solutions in D-dimensions in f(R) gravity
• Sub-Planckian scale and limits for $f(R)$ models
• Scalar-tensor cosmologies in a minisuperspace formulation: a case study
• Multiple fluid theory of cosmic evolution and its thermodynamic analysis
• Asymptotically Schwarzschild solutions in $f(R)$ extension of general relativity
• Matter Creation Cosmologies and Accelerated Expansion
• Phase space analysis of an exponential model in $f(Q)$ gravity including linear dark-sector interactions
• Testing Exponential $f(R)$ Gravity with CMB, DESI-DR2, and Supernova Data
• Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology
• The general expression for $f(T)$ in a charged cylindrical spacetime with diverse dimensions
• Intermediate and Power-Law Inflation in the Tachyon Model with Constant Sound Speed
• New dynamical system approach to Palatini $f(R)$ theories and its application to exponential gravity
• Phenomenological modification of horizon temperature
• One-loop Euclidean Einstein-Weyl gravity in de Sitter universe
• A Note on Gravitational Memory in F(R)-theories and their Equivalent Scalar-Tensor Theories
• Preventing Curvature Singularities in $f(R)$ Dark Energy Models
• Gravitational waveforms from inspiral compact binaries in Hybrid metric-Palatini gravity
• Cosmic expansion history analysis with Hubble parametrization in $Q^n$ gravity
• A Viable model for modified gravity
• $\Lambda$CDM without cosmological constant
• A new approach to modified-gravity models
• A black hole solution of higher-dimensional Weyl-Yang-Kaluza-Klein theory
• Absence of antisymmetric tensor fields : Clue from f(R) model of gravity
• Black Holes and Non-perturbative Gravitational Waves in $f(R)$ Gravity
• Holographic description of $F(R)$ gravity coupled with Axion Dark Matter
• On energy-momentum tensor for gravitational waves in $f(R)$ gravity
• Implications of $f(R)$ gravity on late-time cosmic structure growth through a complete description of density perturbations
• Revisited apparent horizon entropy and GSL in modified gravity
• Ultra-high energy cosmic rays with UFA-15 source model in Bumblebee gravity theory
• The role of longitudinal polarizations in Horndeski and macroscopic gravity: Introducing gravitational plasmas
• Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes
• Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy
• Cosmology in the mimetic higher-curvature $f(R,R_{\mu \nu }{R}^{\mu \nu })$ gravity
• Gravitational Waves Astronomy: a cornerstone for gravitational theories
• Globally Stable Dark Energy in $F(R)$ Gravity
• Observational constraints on a modified-gravity model with an exponential function of the curvature using the expansion history, the RSD, and the Pantheon+SH0ES data
• Modelling Cosmic Rays Flux with Pierre Auger and Telescope Array Data in $\mathbf{f}(\mathbf{R})$ and $\mathbf{f}(\mathbf{Q})$ Theories of Gravity
• Stable massless scalar polarization of f(R) gravity
• New effective theories of gravitation and their phenomenological consequences
• Quantum cosmology in teleparallel gravity with a boundary term
• Cosmological constraints on viable $f(R)$ models using weak lensing
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models
• Non-minimal kinetic coupled gravity: inflation on the Warped DGP brane
• Linearized Treatment of Scalar perturbations in the Asymptotic Cosmological Model