f(R) Gravity and scalar-tensor theory

Abstract

In the present paper we will investigate the relation between scalar-tensor theory and $f(R)$ theories of gravity. Such studies have been performed in the past for the metric formalism of $f(R)$ gravity; here we will consider mainly the Palatini formalism, where the metric and the connections are treated as independent quantities. We will try to investigate under which circumstances $f(R)$ theories of gravity are equivalent to scalar-tensor theory and examine the implications of this equivalence, when it exists.

minor changes to match published version, references added

References in corpus (2)

• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Constraining f(R) gravity in the Palatini formalism

Cited by in corpus (257)

• f(R) Theories Of Gravity
• f(R) theories
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• Testing General Relativity with Present and Future Astrophysical Observations
• Beyond the Cosmological Standard Model
• Extra force in $f(R)$ modified theories of gravity
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Conditions for the cosmological viability of f(R) dark energy models
• Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework
• Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Black holes in scalar-tensor gravity
• Modified gravity and its reconstruction from the universe expansion history
• On the Hubble constant tension in the SNe Ia Pantheon sample
• The Newtonian Limit of F(R) gravity
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Neutron-star mergers in scalar-tensor theories of gravity
• Matter instability in modified gravity
• On the evolution of the Hubble constant with the SNe Ia Pantheon Sample and Baryon Acoustic Oscillations: a feasibility study for GRB-cosmology in 2030
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• On the LCDM Universe in f(R) gravity
• Modified gravity with R-matter couplings and (non-)geodesic motion
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Collapsing spherical stars in f(R) gravity
• Constraints on scalar-tensor models of dark energy from observational and local gravity tests
• Cosmological Constraints on f(R) Acceleration Models
• Phase transition and thermodynamic geometry of Einstein-Maxwell-dilaton black holes
• A viability criterion for modified gravity with an extra force
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• Do f(R) theories matter?
• Traversable Wormholes and Energy Conditions with Two Different Shape Functions in $f(R)$ Gravity
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• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
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• Charged Black Hole Solutions in Gauss-Bonnet-Massive Gravity
• The phase space view of f(R) gravity
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• Baryogenesis in $f(R)$-Theories of Gravity
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• Selected topics in scalar-tensor theories and beyond
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• Constraining Torsion with Gravity Probe B
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• The Palatini side of inflationary attractors
• The dynamics of metric-affine gravity
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• Quasinormal modes of slowly-rotating black holes in dynamical Chern-Simons gravity
• Power-law cosmic expansion in f(R) gravity models
• On the co-existence of matter dominated and accelerating solutions in f(G)-gravity
• Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology?
• Theory of gravitation theories: a no-progress report
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• Post-Newtonian limit of generalized symmetric teleparallel gravity
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Curvature scalar instability in f(R) gravity
• Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces
• Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
• Dynamics of f(R)-cosmologies containing Einstein static models
• Gravitational Perfect Fluid Collapse in f(R) Gravity
• Plane Symmetric Solutions in f(R) Gravity
• Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
• Inflation driven by Einstein-Gauss-Bonnet gravity
• Dynamically induced Planck scale and inflation in the Palatini formulation
• Black hole entropy in scalar-tensor and f(R) gravity: an overview
• Anisotropic Fluid and Bianchi Type III Model in f(R) Gravity
• Energy conditions in f(R) gravity and Brans-Dicke theories
• Accelerating Universe in Modified Theories of Gravity
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• f(R) gravity, torsion and non-metricity
• Gödel-type universes in f(R) gravity
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• Beyond Einstein's General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings
• The Jebsen-Birkhoff theorem in alternative gravity
• Attractor Behaviour in Multifield Inflation
• 6+1 lessons from f(R) gravity
• Noether gauge symmetry for $f(R)$ gravity in Palatini formalism
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
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• Thermodynamic geometry of black holes in f(R) gravity
• A general solution in the Newtonian limit of f(R)- gravity
• Quadratic quantum cosmology with Schutz' perfect fluid
• Modified gravity with $f(R)=\sqrt{R^2-R_0^2}$
• Palatini frames in scalar-tensor theories of gravity
• Constraining Parity Violation in Gravity with Measurements of Neutron-Star Moments of Inertia
• A Unified Approach to Variational Derivatives of Modified Gravitational Actions
• Consistency of $f(R)=\sqrt{R^2-R_0^2}$ Gravity with the Cosmological Observations in Palatini Formalism
• Buchdahl-Bondi limit in modified gravity: Packing extra effective mass in relativistic compact stars
• Palatini f(R) gravity and Noether symmetry
• The dynamics of generalized Palatini Theories of Gravity
• Cosmological perturbations in Palatini modified gravity
• Testing Dark energy models in the light of ${\sigma }_8$ tension
• F(R) gravity's rainbow and its Einstein counterpart
• The metric-affine formalism of f(R) gravity
• Phase transition of charged black holes in massive gravity through new methods
• Tideless Traversable Wormholes surrounded by cloud of strings in $f(R)$ gravity
• Cyclic and heteroclinic flows near general static spherically symmetric black holes
• A reconstruction of modified holographic Ricci dark energy in $f(R,T)$ gravity
• A note on the dynamical features for the extended $f(P)$ cubic gravity
• Corrected Entropy of Friedmann-Robertson-Walker Universe in Tunneling Method
• $f(R)$ global monopole revisited
• Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom
• Multi-Scalar-Tensor Equivalents for Modified Gravitational Actions
• Implications of Palatini gravity for inflation and beyond
• Polarization modes of gravitational waves in Quadratic Gravity
• Cosmological dynamics of fourth order gravity: A compact view
• On stability of a neutron star system in Palatini gravity
• Halo velocity profiles in screened modified gravity theories
• Parity Violating Metric-Affine Gravity Theories
• Hydrodynamic Effects in the Symmetron and $f(R)$-gravity Models
• Cosmological dynamics of brane f(R) gravity
• Polytropic stars in Palatini gravity
• Covariant Effective Action for Loop Quantum Cosmology from Order Reduction
• Dark energy, gravitation and supernovae
• Generalized Israel Junction Conditions for a Fourth-Order Brane World
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• Cosmic Acceleration From Matter-Curvature Coupling
• Compactifying the state space for alternative theories of gravity
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• Observations in Quantum Cosmology
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• Evaluation of cosmological models in $f(R,T)$ gravity in different dark energy scenario
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• Jumping from Metric f(R) to Scalar-Tensor Theories and the relations between their post-Newtonian Parameters
• New class of hybrid metric-Palatini scalar-tensor theories of gravity
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• Cosmological perturbation theory in Generalized Einstein-Aether models
• Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning
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• Geodesic Congruences in the Palatini f(R) Theory
• Charged $AdS$ Black Holes in $4D$ Einstein--Gauss--Bonnet Massive Gravity
• Palatini f(R) gravity as a fixed point
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• Deep connection between f(R) gravity and the interacting dark sector model
• Compatibility between the scalar field models of tachyon, $k$-essence and quintessence in $f(R,T)$ gravity
• Physical Parameters for Stable $f(R)$ Models
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• Clifton's spherical solution in f(R) vacuo harbours a naked singularity
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• Black hole solution and thermal properties in $4D$ AdS Gauss-Bonnet massive gravity
• Stable Charged Radiating Systems Associated with Tilted Observers
• Traversable wormhole in logarithmic $f(R)$ gravity by various shape and redshift functions
• Effects of modified gravity on the turnaround radius in cosmology
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Einstein-Cartan pseudoscalaron inflation
• A study on the interacting Ricci dark energy in $f(R,T)$ gravity
• Implications of non-analytical f(R) gravity at Solar-System scales
• Reconstructing f(R) Gravity from a Chaplygin Scalar Field in de Sitter Spacetimes
• Can the Big Bang Singularity be avoided by a single scalar field?
• Gibbons-Hawking Boundary Terms and Junction Conditions for Higher-Order Brane Gravity Models
• Phase-space of flat Friedmann-Robertson-Walker models with both a scalar field coupled to matter and radiation
• Analytic Electrically Charged Black Holes in $F(R)$-ModMax Theory
• Discrimination between Lambda-CDM, quintessence, and modified gravity models using wide area surveys
• A Non-static Quantum inspired Spacetime in $f(R)$ Gravity: Gravity's Rainbow
• Simulation of geodesic trajectory of charged BTZ black holes in massive gravity
• Dynamical apparent horizons in inhomogeneous Brans-Dicke universes
• Superradiant energy extraction from rotating hairy Horndeski black holes
• Global dynamics in Einstein-Gauss-Bonnet scalar field cosmology with matter
• Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory
• Gravitational collapse in non-minimally coupled gravity: finite density singularities and the breaking of the no-hair theorem
• Constant-Roll Inflation in modified $f(R,\varphi )$ gravity model using Palatini Formalism
• Quantum gravitational corrections from the Wheeler-DeWitt equation for scalar-tensor theories
• Small Anisotropy in Stellar Objects in Modified Theories of Gravity
• Axisymmetric equilibrium models for magnetised neutron stars in Scalar-Tensor Theories
• Cosmological simulations with hydrodynamics of screened scalar-tensor gravity with non-universal coupling
• Linear perturbations in viable f(R) theories
• Observational tests of a two parameter power-law class modified gravity in Palatini formalism
• Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry
• Black hole shadow and acceleration bounds for spherically symmetric spacetimes
• Cosmologically viable generalized Einstein-Aether theories
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Exploring Plane Symmetric Solutions in $f(R)$ Gravity
• Equivalence between Scalar-Tensor theories and $f(R)$-gravity: From the action to Cosmological Perturbations
• Linearized modified gravity theories and gravitational waves physics in the GBD theory
• Constraints on Cubic and $f(P)$ Gravity from the Cosmic Chronometers, BAO & CMB datasets : Use of Machine Learning Algorithms
• Circular geodesics in the field of double-charged dilatonic black holes
• Probing gravity with redshift-space distortions: effects of tracer bias and sample selection
• Cosmic acceleration and $f(R)$ theory: perturbed solution in a matter FLRW model
• Non-minimal coupling influence on the deviation from de Sitter cosmological expansion
• Palatini's cousin: A New Variational Principle
• Classification of Cosmic Scale Factor via Noether Gauge Symmetries
• Gravitational Coupling and Dynamical Reduction of The Cosmological Constant
• Modified Jordan-Brans-Dicke theory with scalar current and the Eddington-Robertson gamma-parameter
• First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies (An explanatory video is available at https://youtu.be/Zi36ooLPhss.)
• Comments on Scalar-Tensor Representation of $f(R)$ Theories
• On the Hyperbolicity and Stability of $3+1$ Formulations of Metric $f(R)$ Gravity
• Constraints on scalar-tensor theories of gravity from observations
• Cosmological dynamics of f(R) models in dynamical system analysis
• Black branes in four-dimensional conformal equivalent theories
• Cosmology of the interacting Tsallis holographic dark energy in $f(R,T)$ gravity framework
• Quantum gravitational corrections to the inflationary power spectra in scalar-tensor theories
• Cosmology of Metric-Affine $R+\beta R^2$ Gravity with Pure Shear Hypermomentum
• Classical Euclidean wormhole solutions in Palatini $f(\tilde{R})$ cosmology
• Ernst formulation of axisymmetric fields in $f(R)$ gravity: applications to neutron stars and gravitational waves
• Stellar structure in $f(R,T)$ gravity: some exact solutions
• Global asymptotic dynamics of the cubic galileon interacting with dark matter
• Energy-momentum squared symmetric Teleparallel gravity: $f(Q,T_{\mu \nu }{T}^{\mu \nu })$ gravity
• On Inflationary Models in f(R,T) Gravity with a Kinetic Coupling Term
• Thawing F(R) cosmology
• An issue with the classification of the scalar-tensor theories of gravity
• Redshift evolution of the Hubble constant: Constraints and new insights from an interacting dark energy model
• de Sitter field equations from quadratic curvature gravity: A group theoretical approach
• Time-Dependent Scalar Fields in Modified Gravities in a Stationary Spacetime
• Addressing the DESI DR2 Phantom-Crossing Anomaly and Enhanced $H_0$ Tension with Reconstructed Scalar-Tensor Gravity
• Multipole analysis for linearized $f(R,\mathcal{G})$ gravity with irreducible Cartesian tensors
• Mimetic-$f(Q)$ gravity: cosmic reconstruction and energy conditions
• Modified gravity with disappearing cosmological constant
• Perturbations of quasi-Newtonian universes in scalar-tensor gravity
• Horizons and singularity in Clifton's spherical solution of f(R) vacuum
• Magnetic black holes in 4$D$ Einstein--Gauss--Bonnet massive gravity coupled to nonlinear electrodynamics
• Cosmological dynamics of interacting dark energy and dark matter in $f(Q)$ gravity
• Multipole analysis for linearized $f(R)$ gravity with irreducible Cartesian tensors
• Principal Components for Model-Agnostic Modified Gravity with 3x2pt
• On the equivalence between $f\left(R\right)$ theories and Einstein gravity
• Energy Conditions in $f(P)$ Gravity
• A Note on the Strong Hyperbolicity of $f(R)$ Gravity with Dynamical Shifts
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Cosmology with Higher-Derivative Gravities
• Some aspects of modified theory of gravity in Palatini formalism unveiled
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Scalar-tensor baryogenesis: a scalar-tensor completion of gravitational baryogenesis
• Dark Energy as a Relic of the Vacuum-Energy Cancellation?
• Notes on f(R) Theories of Gravity
• Non-linear effects in early Universe cosmology
• Softly broken conformal symmetry with higher curvature terms
• Is it possible to separate baryonic from dark matter within the $\Lambda$-CDM formalism?
• Conformal Frame dependence on Cosmological Observations in Scalar-Tensor Theories of Gravity
• Bayesian and Machine-Learning Analyses of Nonminimal $f(Q)$ Gravity and $H_0$ Tension
• Extended Theories of Gravity in cosmological and astrophysical applications
• Conformal coupling associated with the Noether symmetry and its connection with the $\Lambda$CDM dynamics
• Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
• Geometric formulation of $k$-essence and late-time acceleration
• On inflationary parameters in scalar-tensor theories
• Polyakov-like approach to the modified gravity and other geometric theories
• Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid
• New Lorentzian Taub-NUT and Euclidean Eguchi-Hanson Solutions in $f(R)$ gravity
• Linearized Gravity in the Starobinsky Model: Perturbative Deviations from General Relativity
• On the dilation current in metric-affine gravity
• Quasi-Newtonian Cosmological Models in Scalar-Tensor Theories of Gravity
• Cosmic hierarchy in $f(R)$ gravity