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.
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.
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.
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.
Nonminimal curvature-matter coupling produces dynamical dark energy consistent with DESI observations and lunar laser ranging equivalence principle constraints.
A systematic mapping is derived from GUP parameters in minimal-length quantum theory to higher-order curvature coefficients in extended gravity, with an application yielding an upper bound on the minimal measurable length via light deflection corrections.
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.
Parameterized inspiral tests on GW230529 find consistency with GR, with |δφ̂_{-2}| ≲ 8×10^{-5} and ℓ_GB ≲ 0.51 M_⊙ in ESGB theories.
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.
Nonlocal black holes remain consistent with general relativity at the 1.13-sigma level after joint lensing and quasinormal-mode constraints.
citing papers explorer
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Spectrum of pure $R^2$ gravity: full Hamiltonian analysis
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.
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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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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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Tests of General Relativity with GW230529: a neutron star merging with a lower mass-gap compact object
Parameterized inspiral tests on GW230529 find consistency with GR, with |δφ̂_{-2}| ≲ 8×10^{-5} and ℓ_GB ≲ 0.51 M_⊙ in ESGB theories.