Effects of the running gravitational constant on the amount of dark matter

The amount of dark matter in the Milky Way and beyond is examined by taking into account the possible running of the gravitational constant G as a function of distance scale. If the running of G, as suggested by the Asymptotically-Free Higher-Derivative quantum gravity, is incorporated into the calculation of the total dark matter in the galactic halo, the amount of dark matter that is necessary to explain the rotation curve is shown to be reduced by one third compared with the standard calculations. However, this running of G alone cannot reproduce the observed flat behavior of the rotation curve. It is also shown that the running of G cannot explain away the presence of most of the dark matter beyond the scale of f 10 Mpc in the Universe. We also present a pedagogical explanation for the running of G(r) in the region of large scales which is clearly a classical domain.