Modification of the field theory and the dark matter problem
  We present a Modification of the Field Theory in which the topology of space can vary. We show that in MOFT particles lose their point-like character and acquire a specific distribution in space, i.e., each point source is surrounded with a halo which carries charges of all sorts. From the dynamical standpoint such halos can be described by the presence of dark matter or fictitious particles. We show that in MOFT fermions obey a generalized statistics and at scales $r>r_{\min}$ violate the Pauli principle (more than one fermion can occupy the same quantum state). We also demonstrate that in this range the stable equilibrium state corresponds to the fractal distribution of baryons and due to the presence of fictitious particles predicted by MOFT this distribution is consistent with observational limits on $\Delta T/T$. The concept of fictitious particles is then used to explain the origin of the diffuse component in the X-ray background and the origin of scalar Higgs fields. Thus, we show that MOFT allows to relate the rest mass spectrum of elementary particles with cosmological parameters. In conclusion we discuss some open problems in MOFT. 
A. A. Kirillov