卷 23, 编号 1 (2017)

We consider the embedding theory, the approach to gravity proposed by Regge and Teitelboim, in which 4D space-time is treated as a surface in high-dimensional flat ambient space. In its general form, which does not contain artificially imposed constraints, this theory can be viewed as an extension of GR. In the present paper we study the canonical description of the embedding theory in this general form. In this case, one of the natural constraints cannot be written explicitly, in contrast to the case where additional Einsteinian constraints are imposed. Nevertheless, it is possible to calculate all Poisson brackets with this constraint. We prove that the algebra of four emerging constraints is closed, i.e., all of them are first-class constraints. The explicit form of this algebra is also obtained.

It is known that to obtain cosmological solutions consistent with the Hubble law and accelerated expansion, it is necessary to represent space-time in the form of de Sitter space of the first kind, which ismost simply described by a Robertson-Walkermetric having the scale factor with exponential time dependence. In standard general relativity, this solution is obtained by introduction of the cosmological constant Λ associated with dark energy, whose nature is still not clear. It would be of some interest to consider theories allowing one to obtain cosmological-type solutions without using an effective Λ term. This role was at their time claimed by various supergravity theories which are low-energy approximations of superstring theories. However, it was found that in these theories there are so-called no-go theorems which do not allow solutions in the form of de Sitter space of the first kind. It turned out that this problem can be solved in at least two ways. The first way is to admit the possibility of extra time dimensions, as was demonstrated for the ten-dimensional supergravity by Arefyeva et al. Another way is to consider corrections of higher order in the curvature tensor, which is a subject of this paper. As is known, non-chiral ten-dimensional N = 2 supergravity is a low-energy approximation of type IIA superstring theory. In the present paper, we consider the effective action for type IIA superstring theory, taking into account fourthorder curvature corrections. It is shown that in this case, indeed, one can obtain a cosmological solution in the form of de Sitter space, describing an exponential expansion of space without an effective Λ term.

We present a regular spherically symmetric cosmological model of the Lemaıˆ tre class which describes time-dependent and spatially inhomogeneous vacuum dark energy, has the same global structure as de Sitter space-time and is singled out by the holographic principle. The cosmological evolution is governed by quantum evaporation of the cosmological horizon and goes from a large initial value of the cosmological constant to a small final nonzero value which is tightly fixed by the quantum dynamics of the horizon. We study in detail the evolution of scale factors and the behavior of anisotropy during the whole evolution of the universe. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale initial value of the cosmological constant, its final value coincides with that given by observations. The anisotropy parameter grows quickly at the post-inflationary stage, then remains constant for a long time and decreases to the present epoch.

We propose an alternative analysis of black hole entropy from loop quantum gravity (LQG) to reconcile Hawking’s semiclassical results with the statistical mechanics treatment of LQG for all values of the Barbero-Immirzi (BI) parameter. In particular, using the average area of the punctures, we have calculated the corresponding entropy, identified the BI parameter and derived the radiation spectrum in terms of the possible punctures.

We have found a solution to the Einstein equations for the case of radial expansion or radial collapse of a multistring system having a layered structure. It has been shown that the influence of the gravitational field of such multistring system can lead to stable oscillations of a test null string in the vicinity of a fixed (stationary) point in space, which can be regarded as a spatially localized particle with a nonzero effective rest mass. In this case, the ability of multistring systems to create such particles can be considered as a possible alternative to the Higgs mechanism. It has also been noted that for a gas of null strings, creation of particles with nonzero effective rest mass is possible at early stages of the Universe evolution, where due to high pressures and a domain structure of such a gas, mutual penetration of null strings belonging to neighboring domains was unavoidable and could emerge in mass. At later stages, due to expansion of the Universe, such an opportunity could be lost.

The problem of motion of different test particles, charged and spinning objects with a constant spin tensor in different versions of the bimetric theory of gravity is considered by deriving their corresponding path and path deviation equations using a modified Bazanski Lagrangian. Such a Lagrangian, as in the framework of Riemannian geometry, has a capability to obtain path and path deviations of any object simultaneously. This method enables us to derive the path and path deviation equations of different objects orbiting in very strong gravitational fields.

We focus on the large field of a hyperbolic potential form, which is characterized by a parameter f, in the framework of the brane-world inflation in Randall-Sundrum-II model. From the observed form of the power spectrum P_R(k), the parameter f should be of order 0.1m_p to 0.001m_p, the brane tension must be in the range λ ~ (1−10)×10⁵⁷ GeV⁴, and the energy scale is around V₀^1/4 ~ 10¹⁵ GeV. We find that the inflationary parameters (n_s, r, and dn_s/d(ln k) depend only on the number of e-folds N. The compatibility of these parameters with the last Planck measurements is realized with large values of N.