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