Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry

Abstract

We investigate the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained in the framework of modified gravity models with non-minimal matter-geometry coupling. Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of dark matter. The extra-terms in the gravitational field equations with geometry-matter coupling modify the equations of motion of test particles, and induce a supplementary gravitational interaction. Starting from the variational principle describing the particle motion in the presence of the non-minimal coupling, the expression of the tangential velocity of a test particle, moving in the vacuum on a stable circular orbit in a spherically symmetric geometry, is derived. The tangential velocity depends on the metric tensor components, as well as of the coupling function between matter and geometry. The Doppler velocity shifts are also obtained in terms of the coupling function. If the tangential velocity profile is known, the coupling term between matter and geometry can be obtained explicitly in an analytical form. The functional form of this function is obtained in two cases, for a constant tangential velocity, and for an empirical velocity profile obtained from astronomical observations, respectively. Therefore, these results open the possibility of directly testing the modified gravity models with non-minimal coupling between matter and geometry by using direct astronomical and astrophysical observations at the galactic or extra-galactic scale.

8 pages, accepted for publication in PRD

References in corpus (49)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The Cosmological Constant and Dark Energy
• Cosmological Constant - the Weight of the Vacuum
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• Relativistic gravitation theory for the MOND paradigm
• MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on angular scales of 10 arcminutes to 5 degrees
• Extra force in $f(R)$ modified theories of gravity
• Can dark matter be a Bose-Einstein condensate?
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• The Dark Matter Distribution in Disk Galaxies
• Nonminimal coupling of perfect fluids to curvature
• Galaxy Rotation Curves Without Non-Baryonic Dark Matter
• Modified gravity with arbitrary coupling between matter and geometry
• Dark matter in elliptical galaxies: II. Estimating the mass within the virial radius
• Dark energy and dark matter as curvature effects
• Dark matter as a geometric effect in f(R) gravity
• Bimetric MOND gravity
• Dark Matter and Background Light
• The Lagrangian description of perfect fluids and modified gravity with an extra force
• Energy Conditions and Stability in $f(R)$ theories of gravity with non-minimal coupling to matter
• Modified gravity with R-matter couplings and (non-)geodesic motion
• MOND and the "Dearth of Dark Matter in Ordinary Elliptical Galaxies"
• Analysis of Rotation Curves in the framework of R^n gravity
• Can the galactic rotation curves be explained in brane world models?
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• Are galactic rotation curves really flat?
• A viability criterion for modified gravity with an extra force
• The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter
• Thin accretion disks in f(R) modified gravity models
• An alternative approach to the galactic dark matter problem
• Do f(R) theories matter?
• Generalized virial theorem in f(R) gravity
• Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry
• On the non-minimal gravitational coupling to matter
• Galactic Potentials
• Minimum mass of galaxies from BEC or scalar field dark matter
• Dark matter and dark energy as a effects of Modified Gravity
• The virial theorem and the dynamics of clusters of galaxies in the brane world models
• The viability of theories with matter coupled to the Ricci scalar
• Galactic metric, dark radiation, dark pressure and gravitational lensing in brane world models
• Motion of test bodies in theories with nonminimal coupling
• Are galaxies extending?
• Modelling the rotational curves of spiral galaxies with a scalar field
• Scaling behaviour of a scalar field model of dark matter halos
• Scalar field "mini--MACHOs": a new explanation for galactic dark matter
• Halos of Unified Dark Matter Scalar Field
• Non-minimal curvature-matter couplings in modified gravity
• A spherical scalar-tensor galaxy model

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