Alexandr Kirillov

Upon a phenomenological consideration of possible modifications of gravity we introduce a bias operator $ρ_{DM} =\hat{K}ρ_{vis}$. 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

Recently the billiards, forming an important part in theory of dynamical systems with singularities [1,2], found their unexpected application in cosmological problems. It turnes out that a wide class of cosmological models near a singular point, corresponding to the origin of development of our Universe, admits its representation as billiards on the space of constant negative curvature [4,5]. A problem of similar model randomness is reduced to a problem of properties of corresponding billiards. The aim of the present paper is to show the way in which such representation is reached and to present the results obtained within the limits of those models.