**Authors**: Priti Mishra, T. P. Singh

**Date**: 11 Aug 2011

**Abstract**: The standard cold dark matter model is the best fit to cosmological observations and to galaxy rotation curves. However, unless there is a direct detection of dark matter, either in the laboratory or in astronomical observations, one should allow for modified gravity theories such as MOND or Scalar-Tensor-Vector Gravity as possible explanations for flatness of galaxy rotation curves. The STVG theory due to Moffat and collaborators modifies general relativity by the addition of a massive vector field, and the vector field coupling constant, its mass, and the gravitational constant, are dynamical scalar fields. The theory is shown to yield a modified acceleration law which has a repulsive Yukawa component added to the Newtonian law of gravitational acceleration, and which can explain the observed flatness of a large class of galaxy rotation curves by fixing the values of two free parameters [a mass scale and a length scale]. Here we provide a possible insight into the success of the STVG theory, by considering the effect of quadrupole polarization on the averaged gravitational field inside a galaxy, due to the pull of neighboring galaxies. This effect is analogous to the polarization induced modification of averaged electromagnetic fields in a medium, and was studied by Szekeres in the context of propagation of gravitational waves. The study was generalized to the case of a static weak-field approximation by Zalaletdinov and collaborators, who showed that the effect of quadrupole polarization is to modify Poisson's equation for the gravitational potential to a fourth order [biharmonic] equation. We show that, remarkably, the biharmonic equation implies a modified Newtonian acceleration which is of the same repulsive Yukawa form as in the STVG theory, and the corrections could in principle be large enough to explain flatness of the rotation curves.

1108.2375
(/preprints)

2011-08-13, 08:52
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*