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 nontrivial halo appears on scales where the topological structure possesses 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 the topological structure of space.

The observed dark matter phenomenon is attributed to the presence of a gas of wormholes. We show that due to topological polarization effects, the background density of baryons generates non-vanishing values for wormhole rest masses. We infer basic formulae for the scattering cross-section between baryons and wormholes and equations of motion. Such equations are then used for the kinetic and hydrodynamic description of the gas of wormholes. In the Newtonian approximation, we consider the behaviour of density perturbations and show that at very large distances wormholes behave exactly like heavy non-baryonic particles, thus reproducing all features of cold dark matter models. At smaller galactic scales, wormholes strongly interact with baryons and cure the problem of cusps. We also show that collisions of wormholes and baryons lead to some additional damping of the Jeans instability in baryons.

We present the simplest topological classification of wormholes and demonstrate that in open Friedmann models the genus n ≥ 1 wormholes are stable and do not require the presence of exotic forms of matter, or any modification of general relativity. We show that such wormholes may also possess magnetic fields. It is found that when the wormhole gets into a galaxy or a surrounding region, it works as an accelerator of charged particles. If the income of the energy from radiation is small, such a wormhole works simply as a generator of synchrotron radiation. Estimates show that the threshold energy of such an accelerator may vary from sufficiently modest energies of the order of a few Gev, up to enormous energies of the Planckian order and even higher, depending on wormhole parameters.

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We describe in details the procedure how the Lobachevsky space can be factorized to a space of the constant negative curvature filled with a gas of wormholes. We show that such wormholes have throat sections in the form of tori and are traversable and stable in the cosmological context. The relation of such wormholes to the dark matter phenomenon is briefly described. We also discuss the possibility of the existence of analogous factorizations for all types of homogeneous spaces.