Modification of gravity and Dark Matter

Upon a phenomenological consideration of possible modifications of gravity we introduce a bias operator $\rho_{DM} = \hat{K} \rho_{vis}$. We show that the empirical definition of a single bias function $K_{emp}(r,t)$ (i.e., of the kernel for the bias operator) allows to account for all the variety of Dark Matter halos in astrophysical systems. For every discrete source such a bias produces a specific correction to the Newton's potential $\phi = -GM(1/r+F(r,t))$ and therefore all DM effects can be explained as a modification of the gravity law. We also demonstrate that a specific choice of the bias $K \sim 1/r^2$ (which produces a logarithmic correction to the Newton's law $F \sim \ln r$) shows quite a good qualitative agreement with the observed picture of the modern Universe.