Generalized virial theorem in f(R) gravity

Abstract

We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy. The total virial mass is proportional to the effective mass associated with the new geometrical term, which may account for the well-known virial theorem mass discrepancy in clusters of galaxies. The model predicts that the geometric mass and its effects extend beyond the virial radius of the clusters. We also consider the behavior of the galaxy cluster velocity dispersion in f(R) models. Thus, the f(R) virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.

12 pages; references added, minor changes, accepted for publication in JCAP

References in corpus (56)

• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Relativistic gravitation theory for the MOND paradigm
• The Mass Function of an X-Ray Flux-Limited Sample of Galaxy Clusters
• Extra force in $f(R)$ modified theories of gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Conditions for the cosmological viability of f(R) dark energy models
• 1/R gravity and Scalar-Tensor Gravity
• The Average Mass-to-Light Profile of Galaxy Clusters
• Are f(R) dark energy models cosmologically viable ?
• Can dark matter be a Bose-Einstein condensate?
• Late time Cosmological Phase Transition and Galactic Halo as Bose-liquid
• One-loop f(R) gravity in de Sitter universe
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Extended Gravity Theories and the Einstein-Hilbert Action
• Covariant conservation of energy momentum in modified gravities
• The Dark Matter Distribution in Disk Galaxies
• Solar System constraints to general f(R) gravity
• Galaxy Rotation Curves Without Non-Baryonic Dark Matter
• Limit to General Relativity in f(R) theories of gravity
• Dark energy and dark matter as curvature effects
• Solar System tests DO rule out 1/R gravity
• Stability of Cosmological Solution in f(R) Models of Gravity
• Dark Matter and Background Light
• The stability of modified gravity models
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• Cosmological constraints on f(R) gravity theories within the Palatini approach
• Solar System experiments do not yet veto modified gravity models
• MOND and the "Dearth of Dark Matter in Ordinary Elliptical Galaxies"
• Can the galactic rotation curves be explained in brane world models?
• MOND--theoretical aspects
• Are galactic rotation curves really flat?
• Stability of the Einstein static universe in f(R) gravity
• Galaxy Cluster Masses Without Non-Baryonic Dark Matter
• Constraining f(R) theories with the energy conditions
• Dark matter and dark energy as a effects of Modified Gravity
• Linear Potentials and Galactic Rotation Curves
• The virial theorem and the dynamics of clusters of galaxies in the brane world models
• Scales Set by the Cosmological Constant
• Modified gravity and the stability of de Sitter space
• An $f(R)$ gravitation for galactic environments
• Galactic metric, dark radiation, dark pressure and gravitational lensing in brane world models
• Direct Detection Constraints on Superheavy Dark Matter
• Galactic dark matter as a bulk effect on the brane
• On Einstein clusters as galactic dark matter halos
• Cosmic Mass Functions from Gaussian Stochastic Diffusion Processes
• Galaxy Dynamics Predictions in the Nonsymmetric Gravitational Theory
• Galaxy Dynamics Predictions in the Nonsymmetric Gravitational Theory
• Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales
• Bose-Einstein Condensation, Dark Matter and Acoustic Peaks
• Gravitational Equilibrium in the Presence of a Positive Cosmological Constant
• Galactic Metrics

Cited by in corpus (92)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• f(R,T) gravity
• Wormhole geometries in f(R) modified theories of gravity
• Modified gravity with arbitrary coupling between matter and geometry
• Generalized curvature-matter couplings in modified gravity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Dark matter as a geometric effect in f(R) gravity
• Wormhole geometries supported by a nonminimal curvature-matter coupling
• The Lagrangian description of perfect fluids and modified gravity with an extra force
• Nonminimal curvature-matter coupled wormholes with matter satisfying the null energy condition
• Nonminimal torsion-matter coupling extension of f(T) gravity
• Generalized energy conditions in Extended Theories of Gravity
• Dark Matter From f(R,T) Gravity
• An Alternative f (R, T) Gravity Theory and the Dark Energy Problem
• Evolution of cosmological perturbations in Bose-Einstein condensate dark matter
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• Thin accretion disks in f(R) modified gravity models
• Modelling clusters of galaxies by f(R)-gravity
• Energy conditions in modified Gauss-Bonnet gravity
• The virial theorem and the dark matter problem in hybrid metric-Palatini gravity
• Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry
• Thin accretion disk signatures in dynamical Chern-Simons modified gravity
• Dark energy, inflation and dark matter from modified F(R) gravity
• Exact solutions of f(R) gravity coupled to nonlinear electrodynamics
• Wormholes in exponential $f(R,T)$ gravity
• Initial and final de Sitter universes from modified $f(R)$ gravity
• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Geodesic deviation, Raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvature-matter coupling
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Cosmological solutions in generalized hybrid metric-Palatini gravity
• f(G) modified gravity and the energy conditions
• Junction conditions and thin-shells in perfect-fluid $f\left(R,T\right)$ gravity
• Classical tests of general relativity in brane world models
• Gödel-type universes in f(R) gravity
• Beyond Einstein's General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings
• Connecting early and late universe by $f(R)$ gravity
• Latest supernovae constraints on f(R) cosmologies
• Cosmological Constraints from Hubble Parameter on f(R) Cosmologies
• Gravitational collapse of Bose-Einstein condensate dark matter halos
• Two-fluid dark matter models
• Black hole solutions in f(R) gravity coupled with non-linear Yang-Mills field
• Cosmological evolution of finite temperature Bose-Einstein Condensate dark matter
• Astrophysical constraints on extended gravity models
• Solar System constraints on local dark matter density
• Gödel-type universes in Palatini f(R) gravity
• A Dynamical System Analysis of $f(R,T)$ Gravity
• Slowly rotating Bose Einstein Condensate galactic dark matter halos, and their rotation curves
• Testing Bose-Einstein Condensate dark matter models with the SPARC galactic rotation curves data
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Interior Solutions of Fluid Sphere in f(R,T) Gravity Admitting Conformal Killing Vectors
• Jeans instability and turbulent gravitational collapse of Bose-Einstein Condensate dark matter halos
• Casimir effect in Extended Theories of Gravity
• Higher-Derivative $f(R,\square R,T)$ Theories of Gravity
• Generalized virial theorem in Palatini $f(R)$ gravity
• Rotation Curves of Galaxies by Fourth Order Gravity
• Cosmographic constraints on a class of Palatini f(R) gravity
• X-ray clusters of galaxies in conformal gravity
• Could pressureless dark matter have pressure?
• Cosmological anisotropy from non-comoving dark matter and dark energy
• Brane-$f(R)$ gravity and dark matter
• Extended Theories of Gravity with Generalized Energy Conditions
• Future dynamics in f(R) theories
• The simplest parametrization of equation of state parameter in the scalar field Universe
• Nonminimally Coupled Boltzmann Equation I: Foundations
• Maximum turnaround radius in $f(R)$ gravity
• The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature
• Cosmic stringlike objects in hybrid metric-Palatini gravity
• Weak Gravitational Lensing in Fourth Order Gravity
• Gravitation Astrometric Measurement Experiment
• Cosmological Consequences of Exponential Gravity in Palatini Formalism
• The virial theorem in Eddington-Born-Infeld gravity
• The Reconstruction of Constant Jerk Parameter with $f(R,T)$ Gravity in Bianchi-I spacetime
• Virial mass in DGP brane cosmology
• Bose-Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials
• Spherical collapse and virialization in $f(T)$ gravities
• Testing fundamental physics with photon frequency shift
• Beyond Einstein's General Relativity
• Velocity and velocity bounds in static spherically symmetric metrics
• Late-time cosmic acceleration: Dark gravity
• Dwarf Galaxies without Dark Matter: constraints on Modified Gravity
• Can local bulk effects explain the galactic dark matter?
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• Cosmological singularity theorems for $f(R)$ gravity theories
• Self-gravitating systems in Extended Gravity
• An f(R) model for dark matter: rotation curves and gravitational lensing
• Precession shift in curvature based Extended Theories of Gravity and Quintessence fields
• Quasi-Topological Magnetic Brane coupled to Nonlinear Electrodynamics
• Generalized virial theorem in warped DGP brane-world
• Testing the Dark Universe through the Layzer-Irvine Equation