Modification of the field theory and the dark matter problem

We present an extension of the field theory onto the case in which the topology of space can vary. We show that the nontrivial topology of space displays itself in a multivalued nature of all observable fields and the number of fields becomes an additional degree of freedom. In the limit in which topology changes are suppressed, the number of fields is conserved and the Modified Field Theory (MOFT) reduces to the standard field theory where interaction constants undergo an additional renormalization and acquire a dependence on spatial scales. This means 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 as the presence of a dark matter or fictitious particles. When assuming that in the Planck stage of evolution of the Universe topology changes do occur and that the early Universe is in thermodynamic equilibrium, MOFT inevitably predicts the deviation of the law of gravity from Newton’s law in a certain range of scales rmin < r < rmax, in which the gravitational potential shows essentially logarithmic ∼ ln r (instead of 1/r) behavior. In this range, the renormalized value of the gravitational constant G increases and at scales r > rmax acquires a new constant value G ′ ∼ Grmax/rmin. We show that in MOFT fermions obey a generalized statistics and at scales r > rmin 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 ∆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 Higgs fields. Thus, we show that MOFT allows to relate the rest mass spectrum of elementary particles with cosmological parameters. Finally it is demonstrated that in MOFT, in the range rmin < r < rmax the Universe acquires features of a two-dimensional space whose distribution in the observed 3dimensional volume has an irregular character. This provides a natural geometric explanation to the observed fractal distribution of galaxies and the