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

TL;DR

This paper demonstrates that f(R) modified gravity theories can naturally explain galactic rotation curves without dark matter by deriving a specific metric form that accounts for constant tangential velocities.

Contribution

It derives a closed-form metric in f(R) gravity models that explains galactic rotation curves, showing only mild deviations from general relativity are needed.

Findings

f(R) gravity models can reproduce flat rotation curves

The metric form R^{1+n} explains galactic dynamics

Dark matter may be unnecessary in this framework

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.