Fourth Order Gravity, Scalar-Tensor-Vector Gravity, and Galaxy Rotation Curves

TL;DR

This paper explores how fourth order gravity and Scalar-Tensor-Vector Gravity (STVG) can explain galaxy rotation curves without dark matter, showing their modifications to Newtonian gravity resemble MOND and could account for observed galactic dynamics.

Contribution

The paper demonstrates that fourth order gravity naturally produces a Yukawa-like modification of gravity similar to STVG, providing a first principles basis for MOND-like behavior.

Findings

Fourth order gravity yields a Yukawa-type correction to Newtonian gravity.

STVG and fourth order gravity predict similar acceleration scales to MOND.

The models could potentially explain galaxy rotation curves without dark matter.

Abstract

The Lambda-CDM model is the best fit to cosmological data, and to the observed galactic rotation curves. However, in the absence of a direct detection of dark matter one should explore theories such as MOND, and perhaps also modified gravity theories like fourth order gravity and Scalar-Tensor-Vector Gravity [STVG] as possible explanations for the non-Keplerian behaviour of galaxy rotation curves. STVG has a modified law for gravitational acceleration which attempts to fit data by fixing two free parameters. We show that, remarkably, the biharmonic equation which we get in the weak field limit of the field equations in a fourth order gravity theory implies a modification of Newtonian acceleration which is precisely of the same repulsive Yukawa form as in the STVG theory, and the corrections could in principle be large enough to try and explain the observed rotation curves. We also explain how our model provides a first principles understanding of MOND. We also show that STVG and fourth order gravity predict an acceleration parameter $a_0$ whose value is of the same order as in MOND.