Tachyonic instabilities from post-inflation curvature reorganization via quadratic Gauss-Bonnet coupling produce the observed dark matter relic density across wide mass and scale ranges, backed by lattice simulations and a fitting function.
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f(R) Theories Of Gravity
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abstract
Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f(R) theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. We review here f(R) theories of gravity in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented -- metric, Palatini and metric-affine -- and the following topics are discussed: motivation; actions, field equations and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; astrophysical applications.
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background 18representative citing papers
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
Higher-curvature gravities are constructed in which both FLRW backgrounds and linearized scalar perturbations obey at most second-order differential equations.
Hydrodynamical simulations in f(R) gravity using Illustris-TNG find observable 20% effects on high-z HI and stellar power spectra exceeding SKA errors, plus changes in disc galaxy formation.
Explicit planar AdS multi-NUT spacetimes are built via axionic scalars or quadratic gravity, plus planar Kaluza-Klein monopoles with varying magnetic charges.
Constructs charged distorted black hole metric via Harrison transformation and analyzes thermodynamics, geodesics, shadow, and quasinormal modes.
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
Hamiltonian analysis reveals degenerate constraints on singular surfaces in f(R) gravity, leading to empty spectra on certain backgrounds and regularity conditions for dynamical crossings in Starobinsky model.
Semi-analytical calculation of void-galaxy cross-correlation multipoles in Hu-Sawicki f(R) gravity reveals size-dependent deviations from LambdaCDM up to 29.7 percent for small voids, amplified by nonlinear evolution and potentially observable in Stage-IV surveys.
Proposes phase-resolved invariant path-length criteria and a master formula for lower bound on ε_ek in ekpyrotic cosmologies, using BKL suppression and conversion windows as constraints.
Sign-switching dark energy with a transition at z_† fits recent DESI DR2, Planck CMB, and Pantheon+ data better than ΛCDM while raising the inferred Hubble constant and easing the Hubble tension.
In Hu-Sawicki f(R) gravity the redshift-space bispectrum monopole and quadrupole show 2-8% deviations from GR at z=0.7 and k~0.3 h/Mpc with forecasted SNR of 30 and 15 for Euclid.
Stress-tensor deformations of QFTs are mapped to gravitational actions at metric saddles, with bidirectional examples and an induced Newton constant from the one-loop effective action of a massive scalar.
A conservative f(R,T) gravity reformulation decouples the gravitational sector from the microphysical equation of state, enabling computation of neutron star mass-radius relations and tidal deformabilities that satisfy current astrophysical constraints.
A supergravity construction using two chiral superfields embeds arbitrary F(R) gravity as a UV completion of Starobinsky inflation, stabilized by the dilaton and consistent with swampland constraints in a heterotic string example.
For dyonic nonlinear electrodynamics with equal charges, the electromagnetic invariant f vanishes identically, enabling simple gravitating solutions in GR and extended gravity theories.
Ghostly quantum systems can have discrete non-dense energy spectra under classical stability conditions, providing counterexamples to spectral denseness.
Matching conditions in f(R) gravity with restricted generalized Vaidya exteriors force f,R to be linear in areal radius and exclude nontrivial dust collapse for generic viable models, leaving the OS problem unresolved in this sector.
In the Jordan-frame treatment of f(R) gravity the scalaron-photon effective coupling vanishes for m much less than loop-particle masses because the classical-trace diagrams cancel the Fujikawa anomaly term.
Boson stars in teleparallel gravity with nonminimal coupling show negative energy density and energy-condition violation in excited states, with EMRI waveforms potentially detectable by LISA.
In symmetric teleparallel f(Q) gravity with nonminimal EM-nonmetricity coupling, the distance duality relation is dynamically violated, yielding a generalized formula relating observational distances to the Hubble rate.
The Minkowski limit of pure R² gravity is reinterpreted as a thermal singularity via scalar-tensor to Eckart fluid analogy, showing infinite departure from GR rather than recovery.
New FNST scalar-tensor generalization of JNW spacetime is used in GR hydrodynamic simulations of BHL accretion, yielding hydrodynamically generated QPO-like frequencies overlapping observed ranges in stellar-mass compact object systems.
Extends HEFT to f(R) gravity for loop-corrected biased power spectra and outlines emulator extensions from LambdaCDM codes.
citing papers explorer
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Tachyonic gravitational dark matter production after inflation
Tachyonic instabilities from post-inflation curvature reorganization via quadratic Gauss-Bonnet coupling produce the observed dark matter relic density across wide mass and scale ranges, backed by lattice simulations and a fitting function.
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Degenerate higher-order scalar-tensor theories in metric-affine gravity
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
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Cosmological higher-curvature gravities
Higher-curvature gravities are constructed in which both FLRW backgrounds and linearized scalar perturbations obey at most second-order differential equations.
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Realistic simulations of galaxy formation in f(R) modified gravity
Hydrodynamical simulations in f(R) gravity using Illustris-TNG find observable 20% effects on high-z HI and stellar power spectra exceeding SKA errors, plus changes in disc galaxy formation.
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Planar AdS multi-NUT spacetimes and Kaluza-Klein multi-monopoles
Explicit planar AdS multi-NUT spacetimes are built via axionic scalars or quadratic gravity, plus planar Kaluza-Klein monopoles with varying magnetic charges.
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Electrically Charged Distorted Black Holes: Thermodynamics, Particle Dynamics, and Quasinormal Signatures
Constructs charged distorted black hole metric via Harrison transformation and analyzes thermodynamics, geodesics, shadow, and quasinormal modes.
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The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
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On phase-space singular surfaces in $f(R)$ gravity
Hamiltonian analysis reveals degenerate constraints on singular surfaces in f(R) gravity, leading to empty spectra on certain backgrounds and regularity conditions for dynamical crossings in Starobinsky model.
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Unveiling $f(R)$ Gravity with Void-Galaxy Cross-Correlation Multipoles
Semi-analytical calculation of void-galaxy cross-correlation multipoles in Hu-Sawicki f(R) gravity reveals size-dependent deviations from LambdaCDM up to 29.7 percent for small voids, amplified by nonlinear evolution and potentially observable in Stage-IV surveys.
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Phase-resolved field-space distance criteria in ekpyrotic, bouncing and cyclic cosmologies
Proposes phase-resolved invariant path-length criteria and a master formula for lower bound on ε_ek in ekpyrotic cosmologies, using BKL suppression and conversion windows as constraints.
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Sign-Switching Dark Energy: Smooth Transitions with Recent DESI DR2 Observations
Sign-switching dark energy with a transition at z_† fits recent DESI DR2, Planck CMB, and Pantheon+ data better than ΛCDM while raising the inferred Hubble constant and easing the Hubble tension.
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Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid
In Hu-Sawicki f(R) gravity the redshift-space bispectrum monopole and quadrupole show 2-8% deviations from GR at z=0.7 and k~0.3 h/Mpc with forecasted SNR of 30 and 15 for Euclid.
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Geometric realization of stress-tensor deformed field theory
Stress-tensor deformations of QFTs are mapped to gravitational actions at metric saddles, with bidirectional examples and an induced Newton constant from the one-loop effective action of a massive scalar.
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Neutron stars in a conservative $f(R,T)$ gravity
A conservative f(R,T) gravity reformulation decouples the gravitational sector from the microphysical equation of state, enabling computation of neutron star mass-radius relations and tidal deformabilities that satisfy current astrophysical constraints.
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Ultraviolet completion of Starobinsky inflation
A supergravity construction using two chiral superfields embeds arbitrary F(R) gravity as a UV completion of Starobinsky inflation, stabilized by the dilaton and consistent with swampland constraints in a heterotic string example.
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On gravitating dyonic configurations in nonlinear electrodynamics
For dyonic nonlinear electrodynamics with equal charges, the electromagnetic invariant f vanishes identically, enabling simple gravitating solutions in GR and extended gravity theories.
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Quantum mechanics with a ghost: Counterexamples to spectral denseness
Ghostly quantum systems can have discrete non-dense energy spectra under classical stability conditions, providing counterexamples to spectral denseness.
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Oppenheimer-Snyder Collapse in f(R) Gravity : Stalemate or Resolution?
Matching conditions in f(R) gravity with restricted generalized Vaidya exteriors force f,R to be linear in areal radius and exclude nontrivial dust collapse for generic viable models, leaving the OS problem unresolved in this sector.
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Effective scalaron--photon interaction in $f(R)$ gravity
In the Jordan-frame treatment of f(R) gravity the scalaron-photon effective coupling vanishes for m much less than loop-particle masses because the classical-trace diagrams cancel the Fujikawa anomaly term.
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Boson Stars in Teleparallel Gravity with a Nonminimally Coupled Field: The Violation of Energy Conditions and Gravitational Waveforms from EMRIs
Boson stars in teleparallel gravity with nonminimal coupling show negative energy density and energy-condition violation in excited states, with EMRI waveforms potentially detectable by LISA.
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Distance duality relation in symmetric teleparallel gravity
In symmetric teleparallel f(Q) gravity with nonminimal EM-nonmetricity coupling, the distance duality relation is dynamically violated, yielding a generalized formula relating observational distances to the Hubble rate.
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New interpretation of the Minkowski limit of $R^2$ gravity
The Minkowski limit of pure R² gravity is reinterpreted as a thermal singularity via scalar-tensor to Eckart fluid analogy, showing infinite departure from GR rather than recovery.
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QPO-like Signatures and Hydrodynamical Variability in Accretion around a JNW-type Compact Spacetime in Freund-Nambu Scalar-Tensor Gravity
New FNST scalar-tensor generalization of JNW spacetime is used in GR hydrodynamic simulations of BHL accretion, yielding hydrodynamically generated QPO-like frequencies overlapping observed ranges in stellar-mass compact object systems.
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Biased tracers, Hybrid Effective Field Theory and Modified Gravity
Extends HEFT to f(R) gravity for loop-corrected biased power spectra and outlines emulator extensions from LambdaCDM codes.
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Effective Constrained Scalar--Gauss--Bonnet Inflation Motivated by $f(R,\mathcal{G})$ Gravity
An effective constrained scalar-Gauss-Bonnet inflation model yields n_s ≃ 0.958 and r ≃ 2.7×10^{-4} while the exact theory has no propagating scalar degree of freedom.
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Towards a causal effective thermodynamics of scalar-tensor gravity
A causal Israel–Stewart extension of scalar-tensor thermodynamics is constructed via a timelike heat-flux ansatz, enabling the first explicit split of K and T in Bianchi I and FLRW universes.
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Another Look at the Weak-Field Limit of Generalized Hybrid Metric-Palatini Gravity
Generalized hybrid metric-Palatini gravity propagates a massless spin-2 mode and two massive scalars in the weak field; stability requires algebraic conditions on f derivatives at flat space, and planetary data constrain the scalar masses in a hierarchical regime.
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Natural modification of quantum uncertainty, modified gravity, and cosmology
Using FLRW cosmology to connect generalized uncertainty principle modifications to modified gravity shows that only Born-Infeld models remain natural in both settings.
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Non-minimal fluid Lagrangian couplings
Derives modified Einstein and fluid equations for non-minimal matter-Lagrangian-curvature couplings and demonstrates non-equivalence of Schutz and Brown fluid formulations.
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Naturally Light Distortion
A naturally light scalar-like distortion field emerges in generalized gravity and mixes with the Higgs boson.
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Three dimensional black bounces in $f(R)$ gravity
Black bounce geometries exist in 2+1D f(R) gravity with scalar-nonlinear electrodynamics matter, including vanishing scalar curvature solutions whose viability is checked via scalaron mass and energy conditions.
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Static plane symmetric solutions in $f(Q)$ gravity
f(Q) gravity yields Taub-de Sitter-like plane symmetric vacuum solutions, and quadratic models support isotropic slabs where maximum pressure is offset from the center with thickness and pressure increasing for negative α.
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Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model
Nonminimal curvature-matter coupling produces dynamical dark energy consistent with DESI observations and lunar laser ranging equivalence principle constraints.
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Probing Dark Energy Microphysics with kSZ Tomography
Fisher-matrix forecasts for LSST- and CMB-S4-like surveys show kSZ tomography tightens constraints on dark energy parameters w0 and wa by 15% and 32% while assessing detectability of perturbations for different sound speeds.
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Neural Post-Einsteinian Test of General Relativity with the Third Gravitational-Wave Transient Catalog
Neural post-Einsteinian analysis of GWTC-3 finds no GR violation and sets constraints covering both post-Newtonian and beyond-post-Newtonian deviations in a single theory-agnostic setup.
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Improving Slow-Roll Estimates in Starobinsky Inflation Using Analytic Hubble Parameter
Deriving Hubble slow-roll parameters from an analytic approximate Hubble parameter in Starobinsky inflation provides better accuracy than the potential slow-roll approximation, reducing the inferred e-foldings by more than one for ns=0.9649.
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Quantum-Deformed Phase-Space Geometry and Emergent Inflation in Effective Four-Dimensional Spacetime
Quantum deformation of projective phase-space geometry induces a conformally deformed FLRW metric whose time-dependent corrections modify inflationary background equations, slow-roll parameters, and perturbations in a covariant manner.
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Post-Newtonian Constraints on Scalar-Tensor Gravity
A unified post-Newtonian analysis shows that metric vs Palatini scalar-tensor gravity can yield different γ, β and Yukawa suppression, with Palatini f(R̂) recovering GR’s exterior PN limit for point sources.
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Observational constraints on nonlocal black holes via gravitational lensing
Nonlocal black holes remain consistent with general relativity at the 1.13-sigma level after joint lensing and quasinormal-mode constraints.
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Joule-Thomson Effect and Geodesic Structure of Charged AdS Black Holes in f(R,T) Coupled with Nonlinear Electrodynamics
Charge most strongly controls JT inversion and cooling domains of the f(R,T)-NLED AdS black hole; NLED and modified-gravity parameters supply only sub-leading corrections that leave exterior geodesics close to RN-AdS.
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Two-scalar-field $f(R)$ Thick Branes, Gravitational Resonances and Quasinormal Modes
In ghost-free two-scalar f(R) thick branes, internal structure produces no narrow real-axis tensor resonances; quasinormal modes are broad with quality factors 0.9-1.9.
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Equatorial Periodic Orbits and Gravitational Wave Phenomenology around Spherically-symmetric vacuum solution in Freund-Nambu scalar-tensor gravity
Scalar couplings in Freund-Nambu gravity shift ISCO inward and produce detectable temporal dephasing in EMRI gravitational wave bursts while preserving orbit topology.
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Cosmological Constraints on Minimal Cubic Galileon Models in Teleparallel Gravity
Observational constraints on teleparallel cubic Galileon cosmologies with quadratic and exponential potentials show viability for late-time acceleration, with the fixed b1 quadratic case competitive under AIC but not BIC.
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Integrability of $R^2$ gravity cosmological models with radiation
Derives general solution to □R=0 in R² gravity plus radiation in flat FLRW and establishes integrability of the scalar-field and conformal chiral versions.
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Scattering, absorption and greybody factor of scalar particles by Lorentz-violating charged black holes
Partial-wave calculations of scattering cross sections, absorption, and greybody factors for spin-0 particles on charged black holes in bumblebee and Kalb-Ramond Lorentz-violating models.
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Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals
LISA can constrain the Lorentz symmetry breaking parameter ell in bumblebee gravity to O(10^{-4}) uncertainty via EMRI waveform analysis in the AAK framework.
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Energy conditions of bouncing solutions in quadratic curvature gravity coupled with a scalar field
Bouncing solutions in quadratic curvature gravity with a scalar field satisfy null, weak, and dominant energy conditions but violate the strong one when using the scalar-field energy-momentum tensor, while all four conditions are violated near the bounce in the effective tensor formulation.
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Redshift evolution of the Hubble constant: Constraints and new insights from an interacting dark energy model
Modified IDE model with interaction parameter alpha ~0.01 from late-universe data shows H0 decreasing with redshift, tightening to 10^-5 when CMB priors are added.
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On the Metric $f(R)$ gravity Viability in Accounting for the Binned Supernovae Data
f(R) gravity fits binned supernova data for running Hubble constant once an extra dynamical condition ensures a physical scalar field mass.
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On Scalar Cosmological Perturbations in Non-Minimally Coupled Weyl Connection Gravity
Derives cosmological field equations and preliminary scalar perturbation equations for a non-minimally coupled Weyl-connection gravity model that introduces non-metricity to mimic dark sectors.