Chaotic spin precession in anisotropic universes and fermionic dark matter

We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. In the Bianchi-IX universe it acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the veryearly Universe may produce the sterile particles contributing to dark matter.     

A diagram technique for perturbation theory calculations of the effective conductivity of two-dimensional systems

The perturbation theory for calculating the ffective conductivity of the plane consisting of pieces of different conductivities is constructed, and a convenient diagram technique is elaborated for this perturbation theory. It is shown that for the chessboard, perturbative calculations give results that are in agreement with the well-known formula $\sigma _{eff} = \sqrt {\sigma _1 \sigma _2 } $ . The components of the effective conductivity tensor for the anisotropic three-color chessboard are calculated. It is shown that the isotropic (symmetric) part of the effective conductivity calculated up to the sixth order of perturbation theory satisfies the Bruggeman effective medium equation for symmetric three-color structures with equally partitioned components. We also consider an isotropic three-color chessboard with nonequal weights of colors. In this case, the perturbation theory in the fourth order contradicts the results following from the Bruggeman equation for nonequal weights.     

Remarks about the effective conductivity of some three-color tesselations in the plane

The asymptotic formula for the effective conductivity of isotropic three-color (three-conductivity) rhombic tesselation in the plane is obtained for the case when one conductivity is much smaller than the other two. The tentative formula for this rhombic tesselation is suggested and discussed.     

One-loop divergences of the einstein theory with a nonminimally interacting scalar field

We calculate the one-loop divergences of Einstein gravity with a nonlinear nonminimally coupled scalar field. The conformal transformation of the field variables allows us to reduce the Lagrangian to the minimal form which significantly simplifies the application of the Schwinger-DeWitt generalized technique. In the appropriate limit, the end result completely agrees with known results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 121–126, February, 1992.In conclusion, the authors express their gratitude to A. O. Barvinsky for fruitful discussions and support in the course of the work.     

The four-loop beta-function in the Wess-Zumino model

A method for calculating momentum integrals proposed by Chetyrkin and Tkachov is applied to four-loop calculations of the β-function in the Wess-Zumino model.     

Reconstruction of scalar potentials in induced gravity and cosmology

We develop a technique for the reconstruction of the potential for a scalar field in cosmological models based on induced gravity. The potentials reproducing cosmological evolutions driven by barotropic perfect fluids, a cosmological constant, a Chaplygin gas and a modified Chaplygin gas are constructed explicitly.