Extra force in $f(R)$ modified theories of gravity

Abstract

The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.

Revtex4 file, 5 pages. Version to appear in Physical Review D

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• Cosmic acceleration with bulk viscosity in an anisotropic $f(R,L_m)$ background
• Traversable Wormholes in Higher Dimensional Theories of Gravity
• Charged Anisotropic Spherical Collapse in $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ Gravity
• Lessons from $f(R,R_c^2,R_m^2,L_m)$ gravity: Smooth Gauss-Bonnet limit, energy-momentum conservation and nonminimal coupling
• A model independent parametrization of the late time cosmic acceleration: constraints on the parameters from recent observations
• Unraveling gravity beyond Einstein with extended test bodies
• Cosmological Tests of $f(R,G,T)$ Dark Energy Model in FRW Universe
• Dynamical analysis of modified gravity with nonminimal gravitational coupling to matter
• Dark matter as a dynamic effect due to a non-minimal gravitational coupling with matter
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Towards realistic $f(T)$ models with nonminimal torsion-matter coupling extension
• Renormalizability of alternative theories of gravity: differences between power counting and entropy argument
• Screening Mechanism and Late-time Cosmology: Role of a Chameleon-Brans-Dicke Scalar Field
• Inflation with Planck: a survey of some "exotic" inflationary models
• Dynamical systems of cosmological models for different possibilities of $G$ and ${\rho }_{\Lambda }$
• Cosmological implications of the Weyl geometric gravity theory
• Wormhole modeling in $R^2$ gravity with linear trace term
• A non-geodesic motion in the R^-1 theory of gravity tuned with observations
• Quantum kinetic theory of Jeans instability in non-minimal matter-curvature coupling gravity
• Constructions of $f(R,G,\mathcal{T})$ Gravity from Some Expansions of the Universe
• Charged Compact Stars in Extended $f(\mathcal{R},\mathcal{G},\mathcal{T})$ Gravity
• Solar System Constraints on Scalar Tensor Theories with Non-Standard Action
• Noncompactified Kaluza--Klein Gravity
• MOND as the weak field limit of an extended metric theory of gravity with a matter-curvature coupling
• Particle creation and decay in nonminimally coupled models of gravity
• Is dark matter an extra-dimensional effect?
• Observationally constrained accelerating cosmological model with higher power of non-metricity and squared trace
• Cassini and extra force constraints to nonminimally coupled gravity with screening mechanism
• Modified Teleparallel Gravity induced by quantum fluctuations
• Irreversible Geometrothermodynamics of Open Systems in Modified Gravity
• The little rip in classical and quantum $f(R)$ cosmology
• Null Fluid collapse in Rastall theory of gravity
• Gravitational baryogenesis without CPT violation
• Is cosmological data suggesting a nonminimal coupling between matter and gravity?
• Black hole solutions of gravity theories with nonminimal coupling between matter and curvature
• Wormhole solutions under the effect of dark matter in $f(R,L_m)$ gravity
• The study of Kantowski-Sachs perfect fluid cosmological model in modified gravity
• Bose-Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials
• Warm inflation with non-comoving scalar field and radiation fluid
• The 1/c expansion of nonminimally coupled curvature-matter gravity model and constraints from planetary precession
• Inflationary Cosmology in a non-minimal $f(R,T)$ gravity theory using a $RT$ mixing term
• Dissipative quintessence, and its cosmological implications
• Distance-duality in theories with a nonminimal coupling to gravity
• Constraint on dark matter central density in the Eddington inspired Born-Infeld (EiBI) gravity with input from Weyl gravity
• Spherical collapse and virialization in $f(T)$ gravities
• Cosmic Transients, Einstein's Equivalence Principle and Dark Matter Halos
• Smeared Mass Source Wormholes in Modified $f(R)$ Gravity with the Lorentzian Density Distribution Function
• Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory
• Nuclear Limits on Non-Minimally Coupled Gravity
• Magnetized cosmological model with variable deceleration parameter
• Early and Late-time Cosmic Acceleration in Non-minimal Yang-Mills-$f(G)$ Gravity
• Stability, chaos and entrapment of stars in very wide pairs
• Higher-order gravity in higher dimensions: Geometrical origins of four-dimensional cosmology?
• Nonminimal global monopole
• Comments on Scalar-Tensor Representation of $f(R)$ Theories
• Late-time cosmic acceleration: Dark gravity
• Reconstruction of $f(T,\mathcal{T})$ Lagrangian for various cosmological scenarios
• Cosmological constraints on superconducting dark energy models
• $4$-index theory of gravity and its relation with the violation of the energy-momentum conservation law
• Matter really does matter, or Why $f(R,\mathrm{Matter})$ type theories are significant for gravitational physics and cosmology
• Cosmic evolution in the background of non-minimal coupling in $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ Gravity
• ΛCDM suitably embedded in f(R) with a non-minimal coupling to matter
• Upper Limit on the Central Density of Dark Matter in the Eddington inspired Born-Infield (EiBI) Gravity
• Cosmological singularity theorems for $f(R)$ gravity theories
• Extended Geometric Trinity of Gravity
• Motion of pole-dipole and quadrupole particles in non-minimally coupled theories of gravity
• Boltzmann's $H$-theorem, entropy and the strength of gravity in theories with a nonminimal coupling between matter and geometry
• Non-minimal Energy-momentum squared gravity
• Can local bulk effects explain the galactic dark matter?
• Time machines and traversable wormholes in modified theories of gravity
• Constraining Parameters for the Accelerating Universe in $f(R,{\mathcal{L}}_m)$ Gravity
• Notes on diffeomorphisms symmetry of $f(R)$ gravity in the cosmological context
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• On Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in non-standard gravity
• The γ parameter in Brans-Dicke-like (light-)Scalar-Tensor theory with a universal scalar/matter coupling
• Cosmology with higher-derivative matter fields
• Energy-momentum squared symmetric Teleparallel gravity: $f(Q,T_{\mu \nu }{T}^{\mu \nu })$ gravity
• Visible and Dark Matter Profiles in a Non-Minimally Coupled Model
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• Lovelock-Brans-Dicke gravity
• Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity
• Charged black hole solutions in $f(R,T)$ gravity coupled to nonlinear electrodynamics
• Palatini $f(\mathcal{R},{\mathcal{L}}_m,{\mathcal{R}}_{\mu \nu }{T}^{\mu \nu })$ gravity and its Born-Infeld semblance
• Generalized Misner-Sharp energy in the generalized Rastall theory
• Gravitational wave polarizations in nonminimally coupled gravity
• Cosmological Dynamics in Interacting Scalar-Torsion f(T,$\varphi$) Gravity: Investigating Energy and Momentum Couplings
• Second law of thermodynamics in nonminimally coupled gravity
• Cosmological Solutions of the Non-minimally Coupled Weyl Connection Gravity Theories
• Non-Singular Collapse Scenario From Matter-Curvature Coupling
• Singularity problem in f(R) model with non-minimal coupling
• Cosmology in theories with derivative matter coupling
• An Ostrogradsky Instability Analysis of Non-minimally Coupled Weyl Connection Gravity Theories
• Investigation of Bouncing Universe and Phantom Crossing in Modified Gravity Coupled with Weyl Tensor and its Reconstruction
• Pressureless stationary solutions in a Newton-Yukawa gravity model
• Consistent energy-momentum trace couplings of fluids
• The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity
• Using global positioning systems to test extensions of General Relativity
• Observational constraints on viscous cosmology in $f(T,L_m)$ gravity
• Gravitational Waves on Charged Black Hole Backgrounds in Modified Gravity
• Bose-Einstein Condensate Dark Matter Halos confronted with galactic rotation curves
• Growth of cosmic perturbations in the modified $f(R,T)$ gravity
• Mass decomposition of SLACS lens galaxies in Weyl conformal gravity
• Linearized Field Equations and Extra Force in $f(R,{\mathbf{T}}^{(n)})$ Extended Gravity
• A new source for a braneworld cosmological constant from a modified gravity model in the bulk
• Stability analysis and observational constraints in scalar tensor theory
• Modified Gravity with Nonminimal Curvature-Matter Couplings: A Framework for Gravitationally Induced Particle Creation
• Equivalence Principle and Machian origin of extended gravity
• Non-minimal coupling inspires the Dirac cosmological model
• Cosmic acceleration via derivative matter couplings
• The Inflationary Quartic Hilltop Model in a Modified Gravity and Its Comparison with the Observations
• Dynamical systems analysis of a cosmological model with interacting Umami Chaplygin fluid in adiabatic particle creation mechanism: Some bouncing features
• Thermodynamics of the Primordial Universe
• Impulsive gravitational waves of massless particles in extended theories of gravity
• Baryon asymmetry from higher-order matter contributions in gravity
• Modified $f(R,T)$ theory in light of gravitational wave standard sirens
• Theories of gravity with nonminimal matter-curvature coupling and the de Sitter swampland conjectures
• Notes on the Chameleon Brans-Dicke Gravity
• Relativistic MOND from Modified Energetics
• Stability Conditions for the Horndeski Scalar Field Gravity Model
• Generalized virial theorem in warped DGP brane-world
• Observational Restrictions and Slow-Roll D-brane Inflation in the Special $F(\varphi ,T)$ Gravity
• $F(\varphi )T$-Gravity and Inflationary Natural Model
• Charged analog of anisotropic dark energy star in Rastall gravity
• Observational constraints in scalar tensor theory with tachyonic potential
• Quasi-Topological Magnetic Brane coupled to Nonlinear Electrodynamics
• Unified first law for traversable wormholes in non-minimal coupling of curvature and matter
• Dynamical Systems Analysis of $f(R,L_m)$ Gravity Model
• Shadow analysis of an approximate rotating black hole solution with weakly coupled global monopole charge
• Impact of projective curvature tensor in $f\left(R,G\right)$, $f\left(R,T\right)$ and $f\left(R,L_m\right)$-gravity
• Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
• Non-vacuum relativistic extensions of MOND using metric theories of gravity with curvature-matter couplings and their applications to the accelerated expansion of the Universe without dark components
• A Comparative Test of the LCDM and R_h=ct Cosmologies Based on Upcoming Redshift Drift Measurements
• Are Padé approximants suitable for modelling shape functions of traversable wormholes?
• Dynamics of clusters of galaxies with extended $f(\chi )$ gravity
• Revisiting Flat Rotation Curves in Chern-Simons Modified Gravity
• Observational constraints on generic models of non-minimal curvature-matter coupling
• Matter perturbations in Einstein dark energy model
• Null geodesics around a black hole with weakly coupled global monopole charge
• On the classical confinement of test particles to a thin 3-brane in the absence of non-gravitational forces
• Cosmology of the non-local Proca theory
• Wormholes and Time-Machines in Nonminimally Coupled Matter-Curvature Theories of Gravity
• Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{P}\mathcal{T}-$symmetry
• Density perturbations in nonminimally coupled gravity: symptoms of Lagrangian density ambiguity
• Black holes in $f(R,T)$ gravity coupled with Euler-Heisenberg electrodynamics
• Revisiting local-scale invariant gravitational theory
• Spin effects on particle creation and evaporation in $f(R,T)$ gravity
• A Nonminimal Coupling Model and its Short-Range Solar System Impact
• Implications of $f(R)$ gravity on late-time cosmic structure growth through a complete description of density perturbations
• On energy-momentum conservation in non-minimal geometry-matter coupling theories
• A new approach to modified-gravity models
• Weak Field Limit of the Nonminimally Coupled Weyl Connection Gravity
• Cosmological implications and causality in $f(R,L_m,T)$ gravity theory with observational constraints
• Surface configuration in $R+{\mu }^4/R$ gravity
• A Note on Gravitational Memory in F(R)-theories and their Equivalent Scalar-Tensor Theories
• Testing the Dark Universe through the Layzer-Irvine Equation
• On Scalar Cosmological Perturbations in Non-Minimally Coupled Weyl Connection Gravity
• Big Bang Nucleosynthesis constraints on $f(T,L_m)$ gravity
• Is it possible to separate baryonic from dark matter within the $\Lambda$-CDM formalism?
• Singularity Avoidance in Gravitational Collapse of an Inhomogeneous Fluid in Rastall Gravity
• Gravitational Collapse of an Inhomogeneous Fluid in Rastall Theory
• Energy Conditions in Palatini Approach to Modified $f(R)$ Gravity
• Primordial magnetic fields in theories of gravity with non-minimal coupling between curvature and matter
• Constraining runaway dilaton models using joint gravitational-wave and electromagnetic observations
• Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model
• A Modified Gravitational Theory of the Matter Sector of the Type $\varphi (R,T){\mathcal{L}}_m$
• Bayesian and Machine-Learning Analyses of Nonminimal $f(Q)$ Gravity and $H_0$ Tension
• A perturbative approach for the study of compatibility between nonminimally coupled gravity and Solar System experiments
• Maximum mass limit of strange stars in quadratic curvature-matter coupled gravity
• The Contribution of Thermal Effects to the Acceleration of the Deep-Space Pioneer Spacecraft
• Non-singular Bouncing Cosmology in $f(R,G,T)$--Quintom model
• Gravitational waves in Palatini gravity for a non-minimal geometry-matter coupling
• Cosmological sudden singularities in $f(R,T)$ gravity
• Energy Conditions and Stability of Charged Wormholes in $f(R,{\mathcal{L}}_m)$ Gravity: A Comparative Analysis with Compact Objects
• Constraints on Energy Conditions in $f(R,L_m)$ Gravity
• Lagrangian Identity and Mass Evolution of Particle-like Objects in Nonminimally Coupled Gravity
• CLASH-VLT: The Fifth Force in Chameleon Gravity from Joint Lensing and Kinematics Cluster Mass Profiles
• Black hole shadows in nonminimally coupled Weyl connection gravity
• A note on the comments of arXiv:2003.10154 [gr-qc] to our paper Nonminimally Coupled Boltzmann Equation I: Foundations (arXiv:2002.08184 [gr-qc])