In this review we consider in detail different theoretical topics associated with interaction in the dark sector. We study linear and non-linear interactions which depend on the dark matter and dark energy densities. We consider a number of different models (including the holographic dark energy and dark energy in a fractal universe) with interacting dark energy (DE) and dark matter (DM), have done a thorough analysis of these models. The main task of this review was not only to give an idea about the modern set of different models of dark energy, but to show how much can be diverse dynamics of the universe in these models. We find that the dynamics of a Universe that contains interaction in the dark sector can differ significantly from the Standard Cosmological Model (SCM).

We propose a new approach to investigation of quantum manifestations of classical stochasticity (QMCS) in wave functions structure, which can be realized in potentials with two and more local minima. The main advantage of the proposed approach is the possibility to detect QMCS in comparison not different wave functions, but different parts of the same wave function. Efficiency of the approach is demonstrated for two potentials: surface quadrupole oscillations (QO) and lower umbillic catastrophe (UC) D5. Energy spectra and eigenfunctions of classically nonintegrable systems represent the main object of search for QMCS [1,2,3]. It should be pointed out that in analysis of QMCS in the energy spectra the principal role was given to statistical characteristics, i.e. quantum chaos was treated as property of a group of states. In contrast, the choice of a stationary wave function as a basic object of investigation, relates quantum chaos to an individual state. Usual procedure of search for QMCS in wave function implies investigation of distinction in its structure below and above the classical energy of transition to chaos (or other parameters of regularitychaos transition). Such procedure meets difficulties connected with necessity to separate QMCS from modifications of wave functions structure due to trivial changes in its quantum numbers. Up to present time correlations between peculiarities of the classical motion and structure of wave functions were studied mostly for billiardtype systems [4,5,6]. For Hamiltonian systems with non-zero potential energy QMCS were studied either for model wave functions [7] or for potential energy surfaces (PES) with simple geometry [8]. Till now there is practically no information on wave functions structure for generic Hamiltonian systems, including multi-well potentials. Such systems allow existence of the mixed state (MS): different (regular or chaotic) classical regimes coexist in different local minima at fixed energy [9,10]. Aim of our work is to show, that such systems represent optimal object for investigation of QMCS in wave functions structure. Wave functions of MS allow to find QMCS in comparison not different eigenfunctions, but different parts of the same wave function, situated in different regions of configuration space (corresponding 1) e-mail: cherkaskiy@kipt.kharkov.ua to different local minima of the potential). Let us demonstrate this possibility for MS, generated by the deformation potential of surface QO of atomic nuclei [11] and lower UC D 5 [12]. It can be shown [13], that using only the transformation properties of the interaction, the QO potential takes the form PACSwhere a 0 and a 2 are internal coordinates of nuclear surface undergoing the QOSince in the construction of (1) only transformation properties of interaction play role, this expression describes potential energy of surface QO of a charged liquid drop of any nature (for example, a metal cluster [14]), containing specific character of the interaction only in the coefficients C mn . Restricting our...

We consider three cosmological models with linear interaction between the dark components and obtain restrictions on the coupling constant in terms of the cosmographic parameters. It enables us to find constraints on the coupling constant directly based on observational data and to restrict number of numerous models describing interaction in the dark sector.

ABSTRACT. The basis of this work is the scheme for describing the universe, called the "cosmography" entirely based on the cosmological principle. Within the framework of such a scheme the parameters of any model that satisfies the cosmological principle (the universe is homogeneous and isotropic on large scale), can be expressed through cosmographic parameters. We demonstrate a number of advantages of the approach used before traditional methods

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