[en] A review of the cosmological term problem is presented. Baby universe model and the compensating field model are discussed. The importance of more accurate data on the Hubble constant and the Universe age is stressed. 18 refs

[en] Different scenarios of baryogenesis are briefly reviewed from the point of view of possibility of generation of cosmologically interesting amount of antimatter. It is argued that creation of antimatter is possible and natural in many models. In some models not only anti-helium may be produced but also a heavier anti-elements and future observations of the latter would be critical for discovery or establishing stronger upper limits on existence of antimatter. Incidentally a recent observation of iron-rich quasar may present a support to one special model of antimatter creation

[en] A review of the fundamental cosmological problems is given; possible ways of their solution are discussed. A considerable attention is paid to inflationary universe models. It is based on a single assumption that in the history of the universe a period of exponential expansion once existed. If it was sufficiently long the problems of homogeneity, isotropy, horizon, flatness, and relic monopoles could be solved in a unified manner. This is in favour of the model. Against the model is the cosmological term problem and the absence (in the meanwhile) of a consistent in detail of theoretical basis

[en] The problem of the baryon asymmetry of the Universe is considered. It is suggested that the baryon asymmetry of the Universe is generated by black hole evaporation in a specific mechanism proposed by Zeldovich. Net amount of baryons evaporated by a black hole is shown can be unequal to that of antibaryons, even if the baryon charge is microscopically conserved. It is concluded that the discussed mechanism can provide the observed baryon assymetry of the Universe if primary black holes with the mass M=10sup(4+-2)Msub(P), where Msub(P)=10sup(19) GeV is the Planck mass, give noticeable contribution into the total energy density of the Universe

[en] A review of Big Bang Nucleosynthesis (BBN) is presented. Observations of deuterium and helium-4 are discussed. Some BBN restrictions on non-standard physics, especially on neutrino properties and time-variation of fundamental constants are given

[en] A model is proposed in which cosmological constant is cancelled automatically because of the back reaction on it of a scalar field PHI. The cancellation takes place if two conditions are imposed on the theory, namely vanishing of mass selfinteraction of field PHI. The vacuum energy in the framework of the model considered does not dissapear completely. This leads to some modification of the standard universe expansion scheme

[en] It is shown that under general assumptions no static nonsingular solution of the General Relativity equations exists for the graviational field of uniformly flat matter distribution

[en] The problem of the baryon asymmetry in inflationary universe is discussed. It is shown that the baryon asymmetry in inflationary universe under certain constrainsts on masses of superheavy bosons can be larger than that in the standard scenario. An important property of the model considered is that the final baryon asymmetry does not depend on initial conditions in the early universe in contrast to what occUrs in the standard scenario based on (B-L) conserving grand unified theories. The new scenario is realized in the framework of the SU(5) Coleman-Weinberg theory with the symmetry breaking

[en] We show that the recently suggested explanations of cosmic acceleration by the modification of gravity at small curvature suffer violent instabilities and strongly disagree with the known properties of gravitational interactions

[en] A new iteration procedure for the studying of the Stark effect in hydrogen is proposed. The method is very accurate numerically for any value of the electric field strength. The approximate explicit expression obtained for the ground state energy eigenvalue has analytic properties similar to those known for the exact solution. The proposed method can be easily generalized to the excited states too