The cosmological constant of modular closed string field theory. I

We formulate closed string field theory as a quantum theory of modular geometry. We determine the full interacting quantum hamiltonian to all loop orders in perturbation theory. The free action has a new highly non-linear symmetry acting on the string field, and the kinetic operator. Perturbatively we demonstrate that the new theory gives the correct expression for the cosmological constant that is ultraviolet finite to one-loop order.     

Linear perturbations on the cosmological background in the relativistic theory of gravitation: I. Theory

We have derived a system of second-order ordinary differential equations to describe the evolution of small perturbations in the gravitational field and matter characteristics in RTG, with the cosmological solution being a background. These equations are shown to admit the effective gauge invariance, since the graviton mass can be neglected in most cases of interest. The standard expansion in scalar, vector, and tensor components is performed. The equations have been derived for each component.     

Linear perturbations on the cosmological background in the relativistic theory of gravitation: II. Appendix

We have solved the general equations derived in Part I [1] to describe the evolution of the gravitational instability on the background of an oscillating, homogeneous, and isotropic universe in the relativistic theory of gravitation considering a massive graviton. Complete solutions, along with their short-wave and long-wave asymptotics, are given for most distinctive stages of the evolution of the universe, namely, near the turning points corresponding to the maximum and minimum densities, as well as in the radiation-dominated, nonrelativistic, and quintessence stages. In all these cases, except for the turning points, the gauge vectors have been determined for the scalar and vector perturbations, allowing the elimination of wave solutions with a phase velocity that is equal to the speed of light. We conclude that, in principle, the observed structure of the universe could have been formed during a sufficiently large number of its cycles.     

Quantum relativistic theory of an electron in terms of local observables

Dirac equation is reformulated in terms of real local observables, which are mean values of the wave function . The quadrivector current is shown to be a function of the potential vector and of other local observables. The equations describe the evolution of a four dimensional system T, X, Y, Z, and of two scalars, in the coordinate system ct, x, y, z. The current is proportional to the T vector. The Z vector is associated with the spin of the electron. Energy and gauge transformations correspond to rotations in the plane (X, Y). In the presence of a static field, the (real) solutions of the equations appear as eigenfunctions associated with energy eigenvalues. Received 7 September 1998     

Evolution of cosmological perturbations in a brane-universe

In our present Letter, we analyze the impact of the existence of extra dimensions on cosmology, in particular, on the evolution of cosmological perturbations. For a five-dimensional anti-de Sitter spacetime where ordinary matter is confined to a brane-universe, the equations governing the cosmological perturbations are presented in a form very close to the equations of standard cosmology. Two types of corrections appear: corrections due to the unconventional evolution of the homogeneous solution, which change the background-dependent coefficients of the equations, and corrections due to the curvature along the fifth dimension, which act as source terms in the evolution equations.     

Kinetics of interacting gravitational and electromagnetic perturbations in cosmological plasma

The system of Einstein-Maxwell equations and a kinetic equation with a model collision integral for the cosmological plasma is used to study the behavior of gravitational and electromagnetic perturbations in the radiation-dominated stage of expansion of the universe. It is shown that gravitational perturbations are capable of generating electromagnetic fields in the cosmological plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 91–96, January, 1992.     

The cosmological term in the Einstein theory

It is proved that it is necessary to introduce in Einstein's equations a cosmological term proportional to the square of the λ-field strength which is related to the Lorentz group representation class ρμ = 0.     

Fuzzy sets in the theory of measurement of incompatible observables

The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state.