Dark matter as a geometric effect in f(R) gravity

Abstract

We consider the behavior of the tangential velocity of test particles moving in stable circular orbits in f(R) modified theories of gravity. A large number of observations at the galactic scale have shown that the rotational velocities of massive test particles (hydrogen clouds) tend towards constant values at large distances from the galactic center. We analyze the vacuum gravitational field equations in f(R) models in the constant velocity region, and the general form of the metric tensor is derived in a closed form. The resulting modification of the Einstein-Hilbert Lagrangian is of the form R^{1+n}, with the parameter n expressed in terms of the tangential velocity. Therefore we find that to explain the motion of test particles around galaxies requires only very mild deviations from classical general relativity, and that modified gravity can explain the galactic dynamics without the need of introducing dark matter.

9 pages; new references added; references updated, minor improvements, accepted for publication in Astropart. Phys

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• Modified gravity with arbitrary coupling between matter and geometry
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• Wormhole geometries supported by a nonminimal curvature-matter coupling
• Nonminimal curvature-matter coupled wormholes with matter satisfying the null energy condition
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• Classifying and avoiding singularities in the alternative gravity dark energy models
• On the non-minimal gravitational coupling to matter
• Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry
• Palatini formulation of modified gravity with a nonminimal curvature-matter coupling
• Dark energy, inflation and dark matter from modified F(R) gravity
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Accelerating Universe in Modified Theories of Gravity
• Gödel-type universes in f(R) gravity
• Two-fluid dark matter models
• Homogeneous cosmologies in generalized modified gravity
• Restricting Fourth Order Gravity via Cosmology
• Is dark matter an extra-dimensional effect?