Foam-like structure of the Universe

On the quantum stage spacetime had the foam-like structure. When the Universe cools, the foam structure tempers and does not disappear. We show that effects caused by the foamed structure mimic very well the observed Dark Matter phenomena. Moreover, we show that in a foamed space photons undergo a chaotic scattering and together with every discrete source of radiation we should observe a diffuse halo. We show that the distribution of the diffuse halo of radiation around a point-like source repeats exactly the distribution of dark matter around the same source, i.e. the DM halos are sources of the diffuse radiation

Geometric approach to discrete series of unirreps for Vir.

AbstractWe want to realize the discrete series of unirreps for the Virasoro-Bott group Vir (= the central extension of Diff+(S1)) in the space of holomorphic functions on the infinite dimensional Kähler manifold M = Diff+(S1)/S1. The explicit formulae are given for the action of Vir in the space of polynomial functions in the natural complex coordinates on M

On Scattering of Electromagnetic Waves by a Wormhole

We consider scattering of a plane electromagnetic wave by a wormhole. It is found that the scattered wave is partially depolarized and has a specific interference picture depending on parameters of the wormhole and the distance to the observer. It is proposed that such features can be important in the direct search of wormholes

Quasi-Isotropization of the Inhomogeneous Mixmaster Universe Induced by an Inflationary Process

We derive a ``generic'' inhomogeneous ``bridge'' solution for a cosmological model in the presence of a real self-interacting scalar field. This solution connects a Kasner-like regime to an inflationary stage of evolution and therefore provides a dynamical mechanism for the quasi-isotropization of the universe. In the framework of a standard Arnowitt-Deser-Misner Hamiltonian formulation of the dynamics and by adopting Misner-Chitr\`e-like variables, we integrate the Einstein-Hamilton-Jacobi equation corresponding to a ``generic'' inhomogeneous cosmological model whose evolution is influenced by the coupling with a bosonic field, expected to be responsible for a spontaneous symmetry breaking configuration. The dependence of the detailed evolution of the universe on the initial conditions is then appropriately characterized.Comment: 17 pages, no figure, to appear on PR

Billiard Representation for Multidimensional Quantum Cosmology near the Singularity

The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested.Comment: 6 pages, LaTe

Dark matter, dark charge, and the fractal structure of the Universe

It is shown that the observed fractal distribution of galaxies is, in fact, consistent with homogeneity of the Universe and observational limits on $\Delta T/T$, if the presence of dark matter and dark charge predicted by the Modified Field Theory (MOFT) is taken into account. It is also shown that indeed in MOFT the ground state for baryons does correspond to the fractal distribution of baryons with dimension D=2. It is discussed a new scenario of structure formation in which observed structures appear as a result of decay of the primordial fractal distribution of baryons.Comment: 4 pages, a short comment to astro-ph/0202302, Latex, replaced with published version Journal - ref: Phys. Lett. B 535 (2002) pp. 22-2

Dark Matter from a gas of wormholes

The simplistic model of the classical spacetime foam is considered, which consists of static wormholes embedded in Minkowski spacetime. We explicitly demonstrate that such a foam structure leads to a topological bias of point-like sources which can equally be interpreted as the presence of a dark halo around any point source. It is shown that a non-trivial halo appears on scales where the topological structure possesses a local inhomogeneity, while the homogeneous structure reduces to a constant renormalization of the intensity of sources. We also show that in general dark halos possess both (positive and negative) signs depending on scales and specific properties of topological structure of space.Comment: minor corrections (eq. 18

Discrete Dynamics: Gauge Invariance and Quantization

Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and internal symmetries. We describe the main features of the gauge principle relevant to the discrete and finite background. Assuming that continuous phenomena are approximations of more fundamental discrete processes, we discuss -- with the help of a simple illustration -- relations between such processes and their continuous approximations. We propose an approach to introduce quantum structures in discrete systems, based on finite gauge groups. In this approach quantization can be interpreted as introduction of gauge connection of a special kind. We illustrate our approach to quantization by a simple model and suggest generalization of this model. One of the main tools for our study is a program written in C.Comment: 15 pages; CASC 2009, Kobe, Japan, September 13-17, 200

Propagation of cosmic rays in the foam-like Universe

The model of a classical spacetime foam is considered, which consists of static wormholes embedded in Minkowski spacetime. We examine the propagation of particles in such a medium and demonstrate that a single thin ray undergoes a specific damping in the density of particles depending on the traversed path and the distribution of wormholes. The missing particles are scattered around the ray. Wormholes was shown to form DM halos around point-like sources. Therefore, the correlation predicted between the damping and the amount of DM can be used to verify the topological nature of Dark Matter

Symplectic structures associated to Lie-Poisson groups

The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.Comment: 30 page