Non-polynomial quasi-topological gravity models reproduce the standard thermal history, generate dynamical dark energy of geometric origin, and fit supernova, cosmic chronometer, and BAO data competitively with ΛCDM.
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Modified Gravity and Cosmology
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abstract
In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.
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representative citing papers
Regular black holes in the bulk of quasi-topological gravity drive a de Sitter inflationary phase on the brane at small scales, with e-fold number set by the ratio of black hole radius to higher-curvature scale.
Dynamical dark energy imprints O(1) shifts on black hole quasi-normal modes via cosmological hair, enabling constraints at 10^{-2} (LVK) to 10^{-4} (LISA) precision using the cubic Galileon as example.
Stable black hole solutions with cosmological scalar hair are explicitly derived in the cubic Galileon theory, recovering cosmological behavior at large distances and regular short-range dynamics.
Galileon models must obey a void-depth limit tied to expansion history to avoid force breakdowns, excluding ~60% of a linear parameterization's space by z less than or equal to 10.
Eckart heat flux holds for all timelike scalar configurations in F(Φ,X)R + G theories if and only if F_X ≡ 0, reducing the theory to a Jordan-like subclass of Horndeski.
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.
DESI DR2 BAO data exhibits 2.3 sigma tension with CMB in Lambda-CDM but prefers evolving dark energy (w0 > -1, wa < 0) at 3.1 sigma with CMB and 2.8-4.2 sigma when including supernovae.
Higher-curvature gravities are constructed in which both FLRW backgrounds and linearized scalar perturbations obey at most second-order differential equations.
Numerical relativity in the decoupling limit reveals dynamical scalarization and spin-induced (de)scalarization during hyperbolic black hole encounters for both signs of the coupling.
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.
An EFT consistency map transports cosmology-conditioned posteriors from scalar-tensor FLRW backgrounds to black-hole quasinormal-mode kernels, showing tensor-speed effects fall below ringdown detectability while other operators remain potentially active near black holes.
Kinetic screening non-monotonically suppresses or enhances scalar quadrupolar emission from equal-mass neutron star binaries depending on screening radius versus wavelength, with a dipole re-emerging linearly with mass asymmetry.
Ghostly quantum systems can have discrete non-dense energy spectra under classical stability conditions, providing counterexamples to spectral denseness.
A quantum ghost coupled polynomially to a harmonic oscillator has unitary evolution and a stable vacuum because a conserved quantity possesses a positive discrete spectrum.
Unified post-Newtonian analysis reveals that Palatini scalar-tensor theories often face weaker Solar System bounds than metric versions due to stronger Yukawa suppression, with Palatini f(R) reproducing GR limits for point sources unlike metric f(R).
kSZ measurements constrain the gravitational acceleration between galaxy halos to follow g ∝ 1/r^{2.1±0.3}, consistent with Newtonian gravity in ΛCDM.
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.
A lapse function in a 5D anisotropic gravity theory generates a global constraint that cancels Standard Model vacuum energy radiative corrections at all orders in the 4D effective theory.
Quintessence potential decreases monotonically with redshift while kinetic energy crosses zero near z=1, with negative values at intermediate redshifts being statistical artifacts from derivative reconstruction.
In f(R,T) = R + F(T) gravity, nonlinear F makes the averaged modified term differ from F at averaged T, invalidating the common unity-ratio assumption and giving dust nonzero proper pressure.
KiDS-Legacy weak lensing plus CMB data yields a 3 sigma deviation in light deflection from GR in a Lambda CDM background, with the signal driven by large-scale CMB lensing amplitudes.
GW250114 data confirm the remnant is consistent with a Kerr black hole and bound the dominant quadrupolar mode frequency to within a few percent of the GR prediction, with constraints tighter than prior multi-event catalogs.
DESI DR1 full-shape clustering yields Ω_m = 0.2962 ± 0.0095 and σ_8 = 0.842 ± 0.034 in flat ΛCDM, tightening to H_0 = 68.40 ± 0.27 km/s/Mpc with CMB and DESY3, while favoring w_0 > -1, w_a < 0 and limiting neutrino mass sum to < 0.071 eV.
citing papers explorer
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Cosmologically viable non-polynomial quasi-topological gravity: explicit models, $\Lambda$CDM limit and observational constraints
Non-polynomial quasi-topological gravity models reproduce the standard thermal history, generate dynamical dark energy of geometric origin, and fit supernova, cosmic chronometer, and BAO data competitively with ΛCDM.
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Cosmic Inflation From Regular Black Holes
Regular black holes in the bulk of quasi-topological gravity drive a de Sitter inflationary phase on the brane at small scales, with e-fold number set by the ratio of black hole radius to higher-curvature scale.
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Testing Dark Energy with Black Hole Ringdown
Dynamical dark energy imprints O(1) shifts on black hole quasi-normal modes via cosmological hair, enabling constraints at 10^{-2} (LVK) to 10^{-4} (LISA) precision using the cubic Galileon as example.
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Stable black hole solutions with cosmological hair
Stable black hole solutions with cosmological scalar hair are explicitly derived in the cubic Galileon theory, recovering cosmological behavior at large distances and regular short-range dynamics.
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How deep can a cosmic void be? Voids-informed theoretical bounds in Galileon gravity
Galileon models must obey a void-depth limit tied to expansion history to avoid force breakdowns, excluding ~60% of a linear parameterization's space by z less than or equal to 10.
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Eckart heat-flux applicability in $F(\Phi,X)R$ theories and the existence of temperature gradients
Eckart heat flux holds for all timelike scalar configurations in F(Φ,X)R + G theories if and only if F_X ≡ 0, reducing the theory to a Jordan-like subclass of Horndeski.
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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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DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints
DESI DR2 BAO data exhibits 2.3 sigma tension with CMB in Lambda-CDM but prefers evolving dark energy (w0 > -1, wa < 0) at 3.1 sigma with CMB and 2.8-4.2 sigma when including supernovae.
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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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Scalarization and descalarization in hyperbolic encounters of black holes
Numerical relativity in the decoupling limit reveals dynamical scalarization and spin-induced (de)scalarization during hyperbolic black hole encounters for both signs of the coupling.
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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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A cosmology-to-ringdown EFT consistency map for scalar-tensor gravity
An EFT consistency map transports cosmology-conditioned posteriors from scalar-tensor FLRW backgrounds to black-hole quasinormal-mode kernels, showing tensor-speed effects fall below ringdown detectability while other operators remain potentially active near black holes.
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Scalar emission from binary neutron stars in scalar-tensor theories with kinetic screening
Kinetic screening non-monotonically suppresses or enhances scalar quadrupolar emission from equal-mass neutron star binaries depending on screening radius versus wavelength, with a dipole re-emerging linearly with mass asymmetry.
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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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Unitary Time Evolution and Vacuum for a Quantum Stable Ghost
A quantum ghost coupled polynomially to a harmonic oscillator has unitary evolution and a stable vacuum because a conserved quantity possesses a positive discrete spectrum.
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Post-Newtonian Constraints on Scalar-Tensor Gravity
Unified post-Newtonian analysis reveals that Palatini scalar-tensor theories often face weaker Solar System bounds than metric versions due to stronger Yukawa suppression, with Palatini f(R) reproducing GR limits for point sources unlike metric f(R).
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The Atacama Cosmology Telescope: A Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev-Zeldovich Effect
kSZ measurements constrain the gravitational acceleration between galaxy halos to follow g ∝ 1/r^{2.1±0.3}, consistent with Newtonian gravity in ΛCDM.
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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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A Lapse in the Cosmological Constant Problem
A lapse function in a 5D anisotropic gravity theory generates a global constraint that cancels Standard Model vacuum energy radiative corrections at all orders in the 4D effective theory.
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Model-Independent Reconstruction of Quintessence Potential and Kinetic Energy from DESI DR2 and Pantheon+ Supernovae
Quintessence potential decreases monotonically with redshift while kinetic energy crosses zero near z=1, with negative values at intermediate redshifts being statistical artifacts from derivative reconstruction.
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Cosmological Averaging in Nonminimally Coupled Gravity
In f(R,T) = R + F(T) gravity, nonlinear F makes the averaged modified term differ from F at averaged T, invalidating the common unity-ratio assumption and giving dust nonzero proper pressure.
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Evidence for deviation in gravitational light deflection from general relativity at cosmological scales with KiDS-Legacy and CMB lensing
KiDS-Legacy weak lensing plus CMB data yields a 3 sigma deviation in light deflection from GR in a Lambda CDM background, with the signal driven by large-scale CMB lensing amplitudes.
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Black Hole Spectroscopy and Tests of General Relativity with GW250114
GW250114 data confirm the remnant is consistent with a Kerr black hole and bound the dominant quadrupolar mode frequency to within a few percent of the GR prediction, with constraints tighter than prior multi-event catalogs.
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DESI 2024 VII: Cosmological Constraints from the Full-Shape Modeling of Clustering Measurements
DESI DR1 full-shape clustering yields Ω_m = 0.2962 ± 0.0095 and σ_8 = 0.842 ± 0.034 in flat ΛCDM, tightening to H_0 = 68.40 ± 0.27 km/s/Mpc with CMB and DESY3, while favoring w_0 > -1, w_a < 0 and limiting neutrino mass sum to < 0.071 eV.
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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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An Interplay Between Fractional Calculus and Holographic Dark Energy
Introduces Fractional Holographic Dark Energy (FHDE) via fractionally corrected entropy from a modified Wheeler-DeWitt equation and studies its late-time cosmology, field reconstructions, and extensions to modified gravity theories.
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Curvature-induced scalarization of charged AdS black holes
In Einstein-Maxwell-scalar-Gauss-Bonnet theory with negative cosmological constant, RN-AdS black holes exhibit GB scalarization only for restricted coupling ranges, producing single-branch solutions and second-order phase transitions.
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Rotating traversable wormholes and particle dynamics in $f(R,T)$ gravity
Rotating traversable wormholes in f(R,T) gravity are supported by anisotropic fluid satisfying null and strong energy conditions in the slow-rotation approximation, with particle dynamics and gravitational lensing analyzed.
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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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Exploring the Dark Sector: Interacting Radiation in Light of Modern Cosmological Probes
New constraints on dark radiation parameters from recent cosmological datasets show the model alleviates the Hubble tension with SH0ES inclusion while remaining consistent with standard expectations without it.
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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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The impact of evolving dark energy on the Weyl potential measured from the Dark Energy Survey Year 3 data
Evolving dark energy models lower the tension in DES Y3 Weyl potential measurements with GR+ΛCDM predictions to 1.6-2.2σ by changing the theoretical background evolution.
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Cosmological perturbations of TDiff fields
This work constructs perturbation theory for TDiff scalar fields in cosmology, analyzes pressure perturbations and adiabaticity including multi-field interaction effects, and checks stability via effective sound speed.
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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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Cosmological Dynamics of a Non-Canonical Generalised Brans-Dicke Theory
A non-canonical generalized Brans-Dicke theory admits background cosmological solutions matching Lambda CDM characteristics for constant, power-law, and exponential potentials, with dynamics distinct from other scalar-tensor models.
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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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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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$\xi R\phi^2$ non-minimal coupling, and the long range gravitational potential for different spin fields from 2-2 scattering amplitudes
The ξ R φ² non-minimal coupling produces a leading r^{-4} long-range gravitational potential from one-loop 2-2 scattering amplitudes in perturbative quantum gravity with vanishing cosmological constant, with explicit spin dependence for other fields.
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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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Extremalization approach to black hole thermodynamics: perturbations around higher-derivative gravities
The extremalization approach to black hole thermodynamics extends to perturbations around known higher-derivative gravity backgrounds such as Einstein-Gauss-Bonnet, yielding first-order thermodynamic corrections in both flat and AdS spacetimes without explicit perturbed solutions.
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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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Gauge invariant perturbations of $F(T,T_G)$ Cosmology
Derives gauge-invariant perturbation equations for F(T, T_G) cosmology and provides physical interpretations for new contributions in each mode.
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Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
No evidence for deviations from general relativity is found in LIGO-Virgo binary black hole events, with improved constraints on waveform parameters, graviton mass, and ringdown properties.
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Synergy between the gravitational potential decay rate and other structure growth probes in testing gravity
Tomographic DR data added to Σ8 + fσ8 tightens phenomenological MG parameters (μ0, Σ0, η0) and EFT α coefficients by factors of 1.5–2.
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Kinematic Probes of Type-II MMG: Pad\'e Cosmographic Analysis of VCDM
Padé cosmographic analysis with MCMC constrains VCDM parameters using chronometers, DESI BAO, and supernova datasets, showing consistency with ΛCDM and no robust transition feature.
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Lagrangian Extensions of Newtonian Gravity constrained by Solar System tests
Derives post-Newtonian equations from a scalar-extended Newtonian Lagrangian and bounds its free parameter with Solar System observations.
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Quark Stars in Ricci-Determinant Gravity with an Interacting Quark Equation of State
Quark stars in Ricci-Determinant gravity with interacting quark EoS exhibit lower compactness than in GR and become unstable at high central densities when perturbative gravity terms exceed about half the GR contribution.
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Late-Time Cosmology and Structure Formation in Quadratic $f(Q)$ Gravity
Quadratic f(Q) gravity adds an H^4 term to the Friedmann equation and introduces a time-dependent G_eff that suppresses linear growth and halo abundance, offering a modified-gravity route to easing the S8 tension.
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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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Unified dark sector and Hubble-tension alleviation in scalar-vector-tensor gravity
A scalar-vector-tensor theory with late-time-only scalar dynamics provides a mechanism to alleviate the Hubble tension in a unified dark sector framework.