Matter-vacuum coupling cannot eliminate the need for null energy condition violation in static zero-tidal-force traversable topological bridges.
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Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.
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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.
Pure R^2 gravity propagates three degrees of freedom nonlinearly but zero linearly around Minkowski and other traceless-Ricci R=0 spacetimes due to ten second-class constraints becoming first-class upon linearization.
Derives NNLO post-Newtonian tidal contributions to conservative dynamics and ten conserved quantities in massless scalar-tensor theories for spinless sources, with extension to Einstein-scalar-Gauss-Bonnet gravity.
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.
Explicit planar AdS multi-NUT spacetimes are built via axionic scalars or quadratic gravity, plus planar Kaluza-Klein monopoles with varying magnetic charges.
LLM embeddings condition a generative transformer to enable faster convergence, better performance, and generalization to unseen LHC processes using a single model.
Extends scalar-tensor gravity thermodynamics to causal Israel-Stewart model via timelike heat flux ansatz, decoupling T and K while preserving GR equilibrium.
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.
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.
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.
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 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.
Stiff-fluid reheating in Starobinsky inflation fits CMB+BAO at 1 sigma only if excluded by BBN radiation bounds, with remaining 2 sigma space testable by LISA, ET, DECIGO and BBO via blue-tilted GW spectrum.
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.
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.
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.
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.
Derives modified Einstein and fluid equations for non-minimal matter-Lagrangian-curvature couplings and demonstrates non-equivalence of Schutz and Brown fluid formulations.
Only black holes with initial masses in a narrow range formed during inflation survive to the present day, reaching a maximum mass of approximately 1.043 times 10 to the minus 3 solar masses.
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.
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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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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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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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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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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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-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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Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity
Perturbative f(R,G) corrections shift the photon-sphere radius and shadow size, with the Gauss-Bonnet term dominating over mixed curvature contributions.
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Observational tests of \texorpdfstring{$\Lambda(t)$}{Lambda(t)} cosmology in light of DESI DR2
MCMC constraints on two Lambda(t) models with DESI DR2, CC, and Pantheon+ data yield H0 ~72.5-73 km/s/Mpc, Omega_m0 near standard values in joint fits, and n~0.3 indicating mild deviation from LambdaCDM.
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Testing General Relativity with Present and Future Astrophysical Observations
A review summarizing modified theories of gravity, their effects on compact objects, existing bounds from astrophysical observations, and the promise of future gravitational wave tests for strong-field gravity.
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