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

Corrections to the Newton and Coulomb potentials caused by effects of spacetime foam

We use an extended quantum field theory (EQFT) hep-th/9911168 to explore possible observational effects of the spacetime. It is shown that as it was expected the spacetime foam can provide quantum bose fields with a cutoff at very small scales, if the energy of zero - point fluctuations of fields is taken into account. It is also shown that EQFT changes the behaviour of massless fields at very large scales (in the classical region). We show that as $rgg 1/mu$ the Coulomb and Newton forces acquire the behaviour $sim 1/r$ (instead of $1/r^{2}$)

Modification of Newton's law of gravity at very large distances

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 Newtons law in some range of scales $r_{min} r_{max}$ acquires a new constant value $G^{prime}sim Gr_{max}/r_{min}$. 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 $r_{max}$ 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

Corrections to the Newton and Coulomb potentials caused by effects of spacetime foam

We use an extended quantum field theory (EQFT) hep-th/9911168 to explore possible observational effects of the spacetime. It is shown that as it was expected the spacetime foam can provide quantum bose fields with a cutoff at very small scales, if the energy of zero - point fluctuations of fields is taken into account. It is also shown that EQFT changes the behaviour of massless fields at very large scales (in the classical region). We show that as $r\gg 1/\mu$ the Coulomb and Newton forces acquire the behaviour $\sim 1/r$ (instead of $1/r^{2}$).Comment: Latex, 4 page

On topological bias of discrete sources in the gas of wormholes

The model of space in the form of a static gas of wormholes is considered. It is shown that the scattering on such a gas gives rise to the formation of a specific diffuse halo around every discrete source. Properties of the halo are determined by the distribution of wormholes in space and the halo has to be correlated with the distribution of dark matter. This allows to explain the absence of dark matter in intergalactic gas clouds. Numerical estimates for parameters of the gas of wormholes are also obtained

Bilinear identities on Schur symmetric functions

A series of bilinear identities on the Schur symmetric functions is obtained with the use of Pluecker relations.Comment: Accepted to Journal of Nonlinear Mathematical Physics. A reference to a connected result is adde

Effects related to spacetime foam in particle physics

It is found that the existence of spacetime foam leads to a situation in which the number of fundamental quantum bosonic fields is a variable quantity. The general aspects of an exact theory that allows for a variable number of fields are discussed, and the simplest observable effects generated by the foam are estimated. It is shown that in the absence of processes related to variations in the topology of space, the concept of an effective field can be reintroduced and standard field theory can be restored. However, in the complete theory the ground state is characterized by a nonvanishing particle number density. From the effective-field standpoint, such particles are "dark". It is assumed that they comprise dark matter of the universe. The properties of this dark matter are discussed, and so is the possibility of measuring the quantum fluctuation in the field potentials.Comment: 18 pages, minor corrections added to the published varian

Billiard Representation for Multidimensional Cosmology with Intersecting p-branes near the Singularity

Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, and 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 (N-1)-dimensional Lobachevsky space, N = n+l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of (N-2)-dimensional sphere by point-like sources. Some examples with billiards of finite volume and hence oscillating behaviour near the singularity are considered. Among them examples with square and triangle 2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional billiard in ``truncated'' D = 11 supergravity model (without the Chern-Simons term) are considered. It is shown that the inclusion of the Chern-Simons term destroys the confining of a billiard.Comment: 27 pages Latex, 3 figs., submit. to Class. Quantum Gra