Vol 25, No 1 (2019)

For field theories in which no small parameter is available, we use Heisenberg’s quantization procedure to propose a definition of nonperturbative quantum states in terms of the complete set of Green functions. We present the corresponding quantization schemes in the case of Einstein gravity and gauge theories. To illustrate the procedure of quantization, we show that: (1) modified theories of gravity appear as an effective approximation of nonperturbative quantum gravity; (2) the Wheeler-DeWitt equations appear as a sort of approximation of the quantization procedure á la Heisenberg, and (3) it is possible to carry out explicit nonperturbative calculations in quantum chromodynamics, and we obtain the energy spectrum of a quantum monopole and some thermodynamic quantities for a gas of noninteracting quantum monopoles.

A detailed comparative qualitative analysis is carried out for of the evolution of cosmological models based on a doublet of classical and phantom scalar fields with self-action. Just as in the case of a single scalar field, the phase space of such systems becomes multiply connected, there appear ranges of negative total effective energy unavailable for motion. A distinctive feature of the asymmetrical scalar doublet is the time dependence of prohibited ranges’ projections on the phase subspaces of each field.

We discuss the peculiarities of gravitational lensing by spherically symmetric wormholes if they are not symmetric with respect to their throats. It is noticed, in particular, that wormholes always contain the so-called photon spheres, near which the photon deflection angles can be arbitrarily large, but, in general, the throat is such a sphere only for symmetric wormholes. In some cases, photons from outside can cross the throat and return back from a neighborhood of a photon sphere if the latter is located beyond the throat. Two families of generally asymmetric wormhole configurations are considered as examples: (1) anti-Fisher wormholes with a massless phantom scalar field as a source of gravity, and (2) wormholes with a zero Ricci scalar that may be interpreted as vacuum configurations in a brane world. The photon effective potentials and deflection angles for them are found and discussed.

The holographic Ricci dark energy (HRDE) model is studied with bulk viscosity in modified f(R, T) gravity theory. We consider a universe filled with bulk viscous HRDE and pressureless dark matter. We obtain exact solutions and study the evolution of the scale factor and deceleration parameter and their transition from decelerated to accelerated expansion of the universe. The bulk viscosity coefficient is assumed to be constant. The behaviors concerning the cosmic expansion depend on the coupling parameter of f(R, T) and bulk viscous term. We apply two geometric diagnostics, the statefinder {r, s} and Om(z), to discriminate HRDE model from the ΛCDM model. We plot the evolution trajectories in the statefinder plane and Om(z) plane. We find that the viscous HRDE model behaves like quintessence at small values of the bulk-viscous term and like a Chaplygin gas at large values of the bulk-viscous term. However, the model approaches ΛCDM at late times of the evolution of the universe. We explore the obvious violation of energy-momentum conservation in f(R, T) gravity and provide a thermodynamic interpretation of extra terms generated by the nonminimal geometry-matter coupling describing particle production. We observe that the current acceleration of our universe is well explained with bulk viscosity.

We work with the holographic model of interacting dark sector (dark energy plus dark matter) of the universe. The generalized Chaplygin gas model is taken as a Dark Energy (DE) candidate, and it interacts with Cold Dark Matter (CDM) in the framework of linear plus quadratic equation of state (EoS) parameter. We study the effect of interaction on the thermodynamics of the universe. Three interaction parameters of DE-CDM are considered: Γ_ρDE, Γ_ρDM, and Γ(ρ_DE + ρ_DM). We derive the corresponding effective equation of states for these different interaction parameters and analyze the behaviors of the derivative of entropies for DE, CDM and the apparent horizon, which is considered as a boundary of the universe. For this purpose the Generalized Second Law (GSL) of thermodynamics is used in the Friedman- Robertson-Walker (FRW) space to analyze the effect of quadratic terms on the thermodynamics of the universe, and the results are analyzed and compared with the solution for the linear form given in the literature.