On modification of the Newton's law of gravity at very large distances
  We discuss a Modified Field Theory (MOFT) in which the number of fields can vary. It is shown that when the number of fields is conserved MOFT reduces to the standard field theory but interaction constants undergo an additional renormalization and acquire a dependence on spatial scales. In particular, the renormalization of the gravitational constant leads to the deviation of the law of gravity from the Newton's law in some range of scales $r_{\min}<r<r_{\max }$, in which the gravitational potential shows essentially logarithmic $\sim \ln r$ (instead of $1/r$) behavior. In this range, the renormalized value of the gravitational constant $G$ increases and at scales $r > r_{\max}$ acquires a new constant value $G^{\prime}\sim Gr_{\max}/r_{\min}$. From the dynamical standpoint this looks as if every point source is surrounded with a halo of dark matter. It is also shown that if the maximal scale $r_{\max}$ is absent, the homogeneity of the dark matter in the Universe is consistent with a fractal distribution of baryons in space, in which the luminous matter is located on thin two-dimensional surfaces separated by empty regions of ever growing size. 
A.A. Kirillov, D. Turaev