Palatini Approach to Modified Gravity: f(R) Theories and Beyond

Abstract

We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speedup problem, laboratory and solar systems tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other phenomenological aspects related with dark matter/energy and quantum gravity.

50 pages, 6 figures, Invited Review to be submitted to International Journal of Modern Physics D; comments are welcome

References in corpus (60)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• Quantum Nature of the Big Bang: Improved dynamics
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop quantum cosmology of k=1 FRW models
• Metric-affine f(R) theories of gravity
• Limit to General Relativity in f(R) theories of gravity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Are loop quantum cosmos never singular?
• The matter power spectrum in f(R) gravity
• Loop quantum cosmology and the k = - 1 RW model
• Prospects for constraining quantum gravity dispersion with near term observations
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• Closed FRW model in Loop Quantum Cosmology
• Bouncing Cosmologies in Palatini $f(R)$ Gravity
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Violation of the Equivalence Principle in Modified Theories of Gravity
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Spherically symmetric spacetimes in f(R) gravity theories
• f(R) Gravity with Torsion: The Metric-Affine Approach
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Interacting dark energy in $f(R)$ gravity
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Hydrogen atom in Palatini theories of gravity
• Evolution to a smooth universe in an ekpyrotic contracting phase with w > 1
• Curvature scalar instability in f(R) gravity
• Constraints on f(R) Cosmology in the Palatini Formalism
• Viable Palatini-f(R) cosmologies with generalized dark matter
• Dynamical Aspects of Generalized Palatini Theories of Gravity
• CMB and Matter Power Spectra of Early f(R) Cosmology in Palatini Formalism
• Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
• Re-examination of Polytropic Spheres in Palatini f(R) Gravity
• How (Not) to Palatini
• The Cauchy problem of f(R) gravity
• The Cauchy problem for metric-affine f(R)-gravity in presence of perfect-fluid matter
• The interior spacetimes of stars in Palatini f(R) gravity
• Accelerated Cosmological Models in Modified Gravity tested by distant Supernovae SNIa data
• The cosmic snap parameter in f(R) gravity
• Noether Charge and Black Hole Entropy in Modified Theories of Gravity
• Microscopic and Macroscopic Behaviors of Palatini Modified Gravity Theories
• Modified gravity with $f(R)=\sqrt{R^2-R_0^2}$
• Asymptotics and Hamiltonians in a First order formalism
• Consistency of $f(R)=\sqrt{R^2-R_0^2}$ Gravity with the Cosmological Observations in Palatini Formalism
• The dynamics of generalized Palatini Theories of Gravity
• $f(R)$ gravity theories in the Palatini Formalism constrained from strong lensing
• Gödel-type universes in Palatini f(R) gravity
• Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity
• Covariant Effective Action for Loop Quantum Cosmology from Order Reduction
• Surface terms, Asymptotics and Thermodynamics of the Holst Action
• Accelerated expansion in modified gravity with a Yukawa-like term
• Geodesic Congruences in the Palatini f(R) Theory
• Palatini f(R) gravity as a fixed point
• Anisotropic singularities in modified gravity models
• A comment on "The Cauchy problem of f(R)- gravity", Class. Quantum Grav., 24, 5667 (2007), arXiv:0709.4414
• Problems and hopes in nonsymmetric gravity
• Indistinguishable Macroscopic Behaviour of Palatini Gravities and General Relativity
• Observational tests of a two parameter power-law class modified gravity in Palatini formalism
• Gravito-magnetic gyroscope precession in Palatini f(R) gravity

Cited by in corpus (255)

• Beyond the Cosmological Standard Model
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Cosmological inflation in $F(R,\mathcal{G})$ gravity
• Wormholes supported by hybrid metric-Palatini gravity
• Recent Advances on Inflation
• Generalized energy conditions in Extended Theories of Gravity
• Nonperturbative models of quark stars in $f(R)$ gravity
• Swampland Implications of GW170817-compatible Einstein-Gauss-Bonnet Gravity
• Causal Limit of Neutron Star Maximum Mass in $f(R)$ Gravity in View of GW190814
• Observational constraints on cosmological solutions of $f(Q)$ theories
• Reconstructing wormhole solutions in curvature based Extended Theories of Gravity
• Unifying of Inflation with Early and Late Dark Energy Epochs in Axion $F(R)$ Gravity
• Cosmology of hybrid metric-Palatini f(X)-gravity
• Energy conditions bounds on f(T) gravity
• Testing wormhole solutions in extended gravity through the Poynting-Robertson effect
• Aspects of general higher-order gravities
• Unification of Inflation with Dark Energy in $f(R)$ Gravity and Axion Dark Matter
• Role of Tilted Congruence and $f(R)$ Gravity on Regular Compact Objects
• Noether Symmetry Approach in Gauss-Bonnet Cosmology
• Analyzing the $H_0$ tension in $F(R)$ gravity models
• Geometric Inflation and Dark Energy with Axion $F(R)$ Gravity
• $f(R)$ Gravity Inflation with String-Corrected Axion Dark Matter
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Metric-affine Gravity and Inflation
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Born-Infeld gravity and its functional extensions
• Isotropization of locally rotationally symmetric Bianchi-I universe in $f(Q)$-gravity
• Epicyclic frequencies in static and spherically symmetric wormhole geometries
• Scalar induced gravitational waves from primordial black hole Poisson fluctuations in $f(R)$ gravity
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Non-Minimally Coupled Einstein Gauss Bonnet Inflation Phenomenology in View of GW170817
• Unification of a Bounce with a Viable Dark Energy Era in Gauss-Bonnet Gravity
• Hybrid metric-Palatini stars
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Test particle motion around black hole in Einstein-Maxwell-scalar theory
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Gravitational lensing in a topologically charged Eddington-inspired Born-Infeld spacetime
• Inflation in Metric-Affine Quadratic Gravity
• Holographic bounce
• Nonsingular black holes, wormholes, and de Sitter cores from anisotropic fluids
• Maximum Baryon Masses for Static Neutron Stars in $f(R)$ Gravity
• Primordial Gravitational Waves Predictions for GW170817-compatible Einstein-Gauss-Bonnet Theory
• Unveiling the Dynamics of the Universe
• FRW Cosmology in $f(Q,T)$ Gravity
• $k$-essence $f(R)$ Gravity Inflation
• Supermassive Neutron Stars in Axion $F(R)$ Gravity
• Quintessential inflation in Palatini $f(R)$ gravity
• Cosmology in scalar-tensor $f(R,T)$ gravity
• Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case
• Crystal clear lessons on the microstructure of space-time and modified gravity
• Tachyonic Preheating in Palatini $R^2$ Inflation
• Effects of Spatial Curvature on the $f(R)$ Gravity Phase Space: no Inflationary Attractor?
• Palatini $R^2$ Quintessential Inflation
• Astrophysical constraints on extended gravity models
• Implications of Palatini gravity for inflation and beyond
• (Regular) Black holes in conformal Killing gravity coupled to nonlinear electrodynamics and scalar fields
• Pre-Inflationary Bounce Effects on Primordial Gravitational Waves of $f(R)$ Gravity
• Nonsingular black holes in nonlinear gravity coupled to Euler-Heisenberg electrodynamics
• Higgs inflation and teleparallel gravity
• Palatini formulation of the conformally invariant $f\left(R,L_m\right)$ gravity theory
• Universal Inflationary Attractors Implications on Static Neutron Stars
• Neutron Stars in Scalar-tensor Gravity with Quartic Order Scalar Potential
• Dynamic wormhole geometries in hybrid metric-Palatini gravity
• Spontaneous Lorentz symmetry breaking and one-loop effective action in the metric-affine bumblebee gravity
• Little Rip, $\Lambda$CDM and singular dark energy cosmology from Born-Infeld-$f(R)$ gravity
• Generalized Energy-Momentum-Squared Gravity in the Palatini Formalism
• Kinetic Axion $F(R)$ Gravity Inflation
• Effects of the Axion Through the Higgs Portal on Primordial Gravitational Waves During the Electroweak Breaking
• Black holes in five-dimensional Palatini $f(R)$ gravity and implications for the AdS/CFT correspondence
• Landau damping for gravitational waves in parity-violating theories
• Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star
• Modified gravity: a unified approach to metric-affine models
• McVittie solution in f(T) gravity
• Constant-roll $k$-Inflation Dynamics
• Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology
• Absorption by black hole remnants in metric-affine gravity
• Late-Time Cosmology of Scalar-Coupled $f(R,\mathcal{G})$ Gravity
• Cooling process of brown dwarfs in Palatini f(R) gravity
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Cosmology with a new f(R) gravity model in Palatini formalism
• Gravity and $T\bar{T}$ flows in higher dimensions
• Fermi gas and modified gravity
• Constraining alternative theories of gravity using GW$150914$ and GW$151226$
• Maximal Masses of White Dwarfs for Polytropes in $R^2$ Gravity and Theoretical Constraints
• The Classical and Loop Quantum Cosmology Phase Space of Interacting Dark Energy and Superfluid Dark Matter
• Thermodynamics of massless particles in curved spacetime
• $R^2$ Inflation Revisited and Dark Energy Corrections
• Transit String Dark Energy Models in $f(Q)$ Gravity
• Cosmology with Hu-Sawicki gravity in Palatini Formalism
• Emergence of dynamical dark energy from polynomial $f(R)$ theory in Palatini formalism
• Structure of Compact Stars in R-squared Palatini Gravity
• Formalizing Anisotropic Inflation in Modified Gravity
• Kaluza-Klein cosmology from five-dimensional Lovelock-Cartan theory
• Amplification of the Primordial Gravitational Waves Energy Spectrum by a Kinetic Scalar in $F(R)$ Gravity
• Swampland conjectures in hybrid metric-Palatini gravity
• Boson stars in Palatini $f(\mathcal{R})$ gravity
• Canonical Scalar Field Inflation with String and $R^2$-Corrections
• Tensor perturbations of Palatini $f(\mathcal{R})$-branes
• Asymmetric wormholes in Palatini $f(\mathcal{R})$ gravity: Energy conditions, absorption and quasibound states
• Stable Charged Radiating Systems Associated with Tilted Observers
• Black hole solutions in functional extensions of Born-Infeld gravity
• Future dynamics in f(R) theories
• Topological invariant quintessence
• Geodesically complete BTZ-type solutions of $2+1$ Born-Infeld gravity
• Induced gravitational topological term and the Einstein-Cartan modified theory
• $f(Q,L_m)$ gravity, and its cosmological implications
• Primordial black holes in scalar field inflation coupled to the Gauss-Bonnet term with fractional power-law potentials
• New rotating AdS/dS black holes in $\mathrm{f}(\mathrm{R})$ gravity
• Amplification of Primordial Gravitational Waves by a Geometrically Driven non-canonical Reheating Era
• Parameterized non-relativistic limit of stellar structure equations in Ricci-based gravity theories
• Sudden singularities in generalized hybrid metric-Palatini cosmologies
• Generating Rotating Spacetime in Ricci-Based Gravity: Naked Singularity as a Black Hole Mimicker
• $f(R)$-Gravity Generated Post-inflationary Eras and their Effect on Primordial Gravitational Waves
• Generalizing the Constant-roll Condition in Scalar Inflation
• Galactic rotation dynamics in a new $f(\mathcal{R})$ gravity model
• Curvature-matter couplings in modified gravity: from linear models to conformally invariant theories
• Energy-Momentum Squared Gravity: A Brief Overview
• Birth of baby universes from gravitational collapse in a modified-gravity scenario
• Weak-field regime of the generalized hybrid metric-Palatini gravity
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Junction conditions of Palatini $f\left(\mathcal{R},T\right)$ gravity
• Constant-Roll Inflation in modified $f(R,\varphi )$ gravity model using Palatini Formalism
• Uniqueness of the Inflationary Higgs Scalar for Neutron Stars and Failure of non-inflationary Approximations
• FLRW Cosmology in Metric-Affine $F(R,Q)$ Gravity
• Nonsingular black holes in Palatini extensions of General Relativity
• Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity
• Variational principle and boundary terms in gravity à la Palatini
• Gravitational energy-momentum pseudo-tensor in Palatini and metric $f(R)$ gravity
• Gravitational Matter Creation, Multi-fluid Cosmology and Kinetic Theory
• Chiral Gravitational Waves in Palatini Chern-Simons
• ${\mathcal{R}}^2$ Quantum Corrected Scalar Field Inflation
• Further Refining Swampland dS Conjecture in Mimetic f(G) Gravity
• $k$-Inflation-corrected Einstein-Gauss-Bonnet Gravity with Massless Primordial Gravitons
• Charged Compact Stars in Extended $f(\mathcal{R},\mathcal{G},\mathcal{T})$ Gravity
• Configurational Entropy and braneworlds in f(T,B) gravity
• Thin accretion disk images of the black hole in symmergent gravity
• Rescaled Einstein-Hilbert Gravity: Inflation and the Swampland Criteria
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Shape of Dark Energy: Constraining Its Evolution with a General Parametrization
• Myrzakulov $F(T,Q)$ gravity: cosmological implications and constraints
• Cosmological constraints of Palatini $f(\mathcal{R})$ gravity
• Starobinsky Inflation and beyond in Einstein-Cartan Gravity
• Cosmic strings in generalized hybrid metric-Palatini gravity
• Investigating the physical and geometrical parameters of the cosmological models with anisotropic background
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• Non-homogeneous exoplanets in metric-affine gravity
• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
• Some Recent Results on Ricci-Based Gravity Theories
• Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology
• Born-Infeld gravity with a Brans-Dicke scalar
• Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables
• Maxwell extension of $f(R)$ gravity
• Swampland Criteria and Constraints on Inflation in a $f(R,T)$ Gravity Theory
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Late-time Cosmology of scalar field assisted $f(\mathcal{G})$ gravity
• Compact objects in quadratic Palatini gravity generated by a free scalar field
• Constraining Palatini gravity with GR-independent equations of state for neutron stars
• Beyond Einstein's General Relativity
• (3+1)-Formulation for Gravity with Torsion and Non-Metricity II: The Hypermomentum Equation
• Constraints on metric-affine gravity black holes from the stellar motion at the Galactic Center
• Global Portraits of Nonminimal Inflation: Metric and Palatini
• Palatini formulation for gauge theory: implications for slow-roll inflation
• Bouncing cosmological models in a functional form of F(R) gravity
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• The effective Equation of State in Palatini $f(R)$ cosmology
• Inflation with Gauss-Bonnet and Chern-Simons higher-curvature-corrections in the view of GW170817
• New metric-affine generalizations of gravitational wave geometries
• Neutron Stars in f(R)-Gravity and Its Extension with a Scalar Axion Field
• Effective $f(R)$ actions for modified Loop Quantum Cosmologies via order reduction
• $R^2$ Gravity Effects on the Kinetic Axion Phase Space
• Collapsing dynamics of relativistic fluid in modified gravity admitting a conformal Killing vector
• Kinetic Axion Dark Matter in String Corrected $f(R)$ Gravity
• Higher order gravities and the Strong Equivalence Principle
• Fundamental Physics and Cosmology with TianQin
• Anisotropic Born-Infeld-f(R) Cosmologies
• Polarization modes of gravitational waves in general Einstein-vector theory
• Inflation with exotic kinetic terms in Einstein-Chern-Simons gravity
• Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory
• Neutron Stars in Palatini $R+\alpha R^2$ and $R+\alpha R^2+\beta Q$ Theories
• Constraining fundamental parameters in modified gravity using Gaia-DR2 massive white dwarf observation
• Tolman-Ehrenfest-Klein Law in non-Riemannian geometries
• A diffeomorphism invariant family of metric-affine actions for loop cosmologies
• Hybrid metric-Palatini Higgs inflation
• The Equivalence Principle as a Noether Symmetry
• New Black Hole Solutions of Second and First Order Formulations of Nonlinear Electrodynamics
• Scalar Mode Quadrupole Radiation from Astronomical Sources in $F(R)$ Modified Gravity
• Gödel and Gödel-type solutions in the Palatini $f(R,T)$ gravity theory
• Unification of the inflation with late-time acceleration in Born-Infeld-$f(R)$ gravity
• Palatini $f(R)$ gravity tests in the weak field limit: Solar System, seismology and galaxies
• Stellar structure in $f(R,T)$ gravity: some exact solutions
• A class of simple bouncing and late-time accelerating cosmologies in f(R) gravity
• Self-gravitating systems in Extended Gravity
• Inflation in non-local hybrid metric-Palatini gravity
• Novel electrically charged wormhole, black hole and black bounce exact solutions in hybrid metric-Palatini gravity
• Kinematics in Metric-Affine Geometry
• Cosmological implications of Born-Infeld-$f(R)$ gravity
• Tsallis holographic dark energy model with event horizon cutoff in modified gravity
• Primordial black holes in SB SUSY Gauss-Bonnet inflation
• Evolving Wormholes in a Cosmological Background
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Modified Gravity with Nonminimal Curvature-Matter Couplings: A Framework for Gravitationally Induced Particle Creation
• Deviations from the von Laue condition: Implications for the on-shell Lagrangian of particles and fluids
• Kantowski-Sachs cosmology in scalar-torsion theory
• Gravitational waves in the extended theory of gravity
• A polynomial affine model of gravity: after ten years
• Precession shift in curvature based Extended Theories of Gravity and Quintessence fields
• Probing Dark Energy Properties in $fQ,C)$ Gravity with FLRW Cosmological Models
• Determinantal Born-Infeld Coupling of Gravity and Electromagnetism
• Propagation and lensing of gravitational waves in Palatini $f(\hat{R})$ gravity
• Equation of state of dark energy in f(R) gravity
• Friedmann cosmology with hyperfluids
• About the (in)equivalence between holonomic versus non-holonomic theories of gravity
• Compact scalar field solutions in EiBI gravity
• Spacetime Curvature as a Probe of Exotic Core Phases in Neutron Stars within Modified Gravity
• Thermodynamic Behavior of Time-Dependent Wormholes in Palatini $f(R)$ Gravity
• Geodesic deviation equation in generalized hybrid Metric-Palatini gravity
• Contemplating the fate of modified gravity
• On the equivalence between $f\left(R\right)$ theories and Einstein gravity
• Generalized Einstein-Maxwell field equations in the Palatini formalism
• Legendre scalarization in gravity and cosmology
• Gravitational wave propagation in generalized hybrid metric-Palatini gravity
• Born-Infeld-$f(R)$ gravity with de Sitter solutions
• The Role of Torsion in Trans-Planckian Physics
• Inflation from entropy
• Modified Palatini action that gives the Einstein-Maxwell theory
• Robustness of predicted CMB fluctuations in Cartan $F(R)$ gravity
• The Universe according to DESI results
• New dynamical system approach to Palatini $f(R)$ theories and its application to exponential gravity
• Gravitational duality, Palatini variation and boundary terms: A synopsis
• Cosmologies in $f(R,{\mathcal{L}}_m)$ theory with non-minimal coupling between geometry and matter
• Thick brane in Palatini formalism with a non-minimally coupled bulk scalar field
• Born-Infeld-f(R) black holes
• Quintessence dark energy model in non-linear $f(Q)$ theory with bulk-viscosity
• Holographic description of $F(R)$ gravity coupled with Axion Dark Matter
• Mixed gauge-gravity term and proper time
• Non-metricity signatures on the Higgs boson signal strengths at the LHC
• Gödel-type solutions in hybrid metric-Palatini gravity
• Flat and bent branes in Born-Infeld-like scalar field models
• Primordial Cosmology of an Emergent-like Universe from Modified Gravity: Reconstruction and Phenomenology Optimization with a Genetic Algorithm
• Generalized Chern-Pontryagin models
• Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism
• Gravitational waves in Palatini gravity for a non-minimal geometry-matter coupling
• Investigating the effects of gravitational lensing by Hu-Sawicki $\mathbf{f}(\mathbf{R})$ gravity black holes
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity
• A Covariant Curvature-History Field Formulation for State-Dependent Infinite-Derivative Gravity
• The stability of the de-Sitter universe in nonlocal gravity
• Cosmological sudden singularities in $f(R,T)$ gravity
• Extended Theories of Electrodynamics in $f(R)$ Gravity
• Torsion-Induced Modification to Friedmann Equations in $AdS{L}_4$ Gauged Gravity
• A Modified Gravitational Theory of the Matter Sector of the Type $\varphi (R,T){\mathcal{L}}_m$
• New effective theories of gravitation and their phenomenological consequences
• The role of longitudinal polarizations in Horndeski and macroscopic gravity: Introducing gravitational plasmas