Abstract
Abstract 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 rmin rmax acquires a new constant value G′∼Grmax/rmin. 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 rmax 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.
Highlights
It is well established that dark matter gives the leading contribution to the matter density of the Universe
We show that in the case when the number of fields is conserved Modified Field Theory (MOFT) reduces to the standard field theory in which interaction constants undergo an additional renormalization and, as a consequence, may acquire a dependence on spatial scales
The logarithmic behavior of the effective field potentials appears in the thermodynamically equilibrium state at the low temperature, as a by-product of a non-trivial structure of MOFT. In this manner we have shown that in the case when the number of fields is conserved MOFT reduces to the standard field theory in which interaction constants undergo a renormalization and, in general, acquire a dependence on spatial scales
Summary
It is well established that dark matter gives the leading contribution to the matter density of the Universe (e.g., see [1]). Where b is the baryon number and Λ defines a characteristic scale r0 ∼ 1/Λ ∼ 5 kpc on which this potential starts to dominate over gravity This model contains basic features of MOND (at least roughly) but fails when confronting with gravitational lensing by clusters. We note that if this additional potential cuts off at very large distances, the effects of the extra potential will not, be distinguishable from that of dark matter It appears that the standard particle physics does not possess fields able to produce interactions which has a range of scales with logarithmic behavior. In the present Letter we, show that the logarithmic potentials appear naturally in the so-called Modified Field Theory (MOFT) suggested in Ref. We show that in MOFT such kind of assumptions leads almost immediately to the logarithmic growth of the gravitational potential in some range of scales
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