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A model for the late-time accelerated expansion of the universe is considered where a van der Waals fluid interacting with matter plays the role of dark energy. The transition towards this phase in the cosmic evolution history is discussed in detail and, moreover, a complete classification of the future finite-time singularities is obtained for six different possible forms of the non-gravitational interaction between dark energy (the van der Waals fluid) and dark matter. This study shows, in particular, that a universe with a non-interacting three-parameter van der Waals fluid can evolve into a universe characterized by a Type IV~(Generalized Sudden) Singularity. On the other hand, for certain values of the parameters, exit from the accelerated expanding phase is possible in the near future, what means that the expansion of the universe in the future could become decelerated. On the other hand, our study shows that space can be divided into different regions. For some of them, in particular, the non-gravitational interactions $Q = 3 H b \rho_{de}$, $Q = 3 H b \rho_{dm}$ and $Q = 3 H b (\rho_{de} + \rho_{de})$ may completely suppress future finite-time singularity formation, for sufficiently high values of $b$. On the other hand, for some other regions of the parameter space, the mentioned interactions would not affect the singularity type, namely the Type IV singularity generated in the case of the non-interacting model would be preserved. A similar conclusion has been archived for the cases of $Q = 3 b H \rho_{de}\rho_{dm}/(\rho_{de}+\rho_{dm})$, $Q = 3 b H \rho_{dm}^{2}/(\rho_{de}+\rho_{dm})$ and $Q = 3 b H \rho_{de}^{2}/(\rho_{de}+\rho_{dm})$ non-gravitational interactions, with only one difference: the $Q = 3 b H \rho_{dm}^{2}/(\rho_{de}+\rho_{dm})$ interaction will change the Type IV singularity of the non-interacting model into a Type II~(The Sudden) singularity.

In this paper a study of the accelerated expansion problem of the large scale universe is presented. To derive Friedmann like equations, describing the background dynamics of the recent universe we take into account, that it is possibile to interpret the spacetime dynamics as an emergent phenomenon. It is a consequence of the deep study of connection between gravitation and thermodynamics. Considered models are based on phenomenological modifications of the horizon temperature. In general, there are various reasons to modify the horizon temperature and one of them can be related to the feedback from the spacetime on the horizon, which will generate additional heat. In order to constraint the parameters of the models we use $Om$ analysis and the constraints on this parameter at $z=0.0$, $z=0,57$ and $z=2.34$.

In this paper we will demonstrate possible existence of more exotic forms of interaction taking into account, that dark energy can be parametrized as a varying polytropic uid suggested recently by the first author. On going research in both directions, i.e. dark energy and non-gravitational interaction, opens very interesting perspectives for solving the problems which are related to the accelerated expansion of the Universe. The fact that available observational data allows to parametrize the dark side of our Universe in form of interacting dark uids is not less surprising, than the accelerated expansion itself. Therefore, the consideration of new forms of non-gravitational interactions in modern cosmology still is one of the actual topics and requires deep and systematic research. This fact motivates us to consider various new forms of non-gravitational logarithmic interactions and study their cosmological consequences. Appropriate classification of the models is presented in the light of actively discussed Om analysis and the result for the Hubble parameter measured at z = 2:34 in BOSS experiment., Comment: 13 pages, 6 figures, 5 tables

Subject of our study it is the accelerated expansion of the large scale universe, where a varying ghost dark energy can take the role of the dark energy. The model of the varying ghost dark energy considered in this work it is a phenomenological modification of the ghost dark energy. Recently, three other phenomenological models of the varying ghost dark energy have been suggested and the model considered in this work will complete the logical chain of considered modifications. The best fit of theoretical results to the luminosity distance, has been used to obtain preliminary constraints on the parameters of the models. This does help us to reduce amount of discussion. On the other hand, detailed comparison of theoretical results with observational data has been left as a subject of another discussion elsewhere. Moreover, a look to considered models via $Om$ and statefinder hierarchy analysis is presented and discussed for different forms of interaction between the varying ghost dark energy and cold dark matter.

In this paper we consider the models of the accelerated expanding large scale universe~(according to general relativity) containing a generalized holographic dark energy with a Nojiri - Odintsov cut - off. The second component of the darkness is assumed to be the pressureless cold dark matter according to observed symmetries of the large scale universe. Moreover, we assume specific forms of the interaction between these two components and besides the cosmographic analysis, we discuss appropriate results from $Om$ and $Om3$ analysis and organize a closer look to the models via the statefinder hierarchy analysis, too. In this way we study mainly impact of the interaction on the dynamics of the background of our universe~(within specific forms of interaction). To complete the cosmographic analysis, the present day values of the statefinder parameters $(r,s)$ and $(\omega^{\prime}_{de}, \omega_{de})$ has been estimated for all cases and the validity of the generalized second law of thermodynamics is demonstrated. Our study showed that theoretical results from considered phenomenological models are consistent with the available observational data and symmetries., Comment: Accepted in Astrophysics and Space Science

The goal of this paper is to study new cosmological models where the dark energy is a varying Chaplygin gas. This specific dark energy model with non-linear EoS had been often discussed in modern cosmology. Contrary to previous studies, we consider new forms of non-linear non-gravitational interaction between dark matter and assumed dark energy models. We applied the phase space analysis allowing understanding the late time behavior of the models. It allows demonstrating that considered non-gravitational interactions can solve the cosmological coincidence problem. On the other hand, we applied Bayesian Machine Learning technique to learn the constraints on the free parameters. In this way, we gained a better understanding of the models providing a hint which of them can be ruled out. Moreover, the learning based on the simulated expansion rate data shows that the models cannot solve the $H_{0}$ tension problem., Comment: New section has been added. Old results have been updated. 19 pages, 4 figures

The goal of this paper is to discuss phase space analysis of some interacting Chaplygin gas models in General Relativity. Chaplygin gas is one of the fluids actively considered in modern cosmology due to the fact that it is a joint model of dark energy and dark matter. In this paper we have considered various forms of interaction term Q including linear and non linear sign changeable interactions. For each case late time attractors for the field equations are found.

In this paper, we consider two-component dark energy models in Lyra manifold. The first component is assumed as a quintessence field while the second model may be a viscous polytropic gas, a viscous Van der Waals gas or a viscous modified Chaplygin gas. We also consider the possibility of interaction between components. By using numerical analysis, we study some cosmological parameters of the models and compare them with observational data., Comment: Accepted by Advances in High Energy Physics. arXiv admin note: text overlap with arXiv:1303.3436 by other authors

In this paper, we consider an effective quintessence scalar field with a power-law potential interacting with a $P_{b}=\xi q\rho_{b}$ barotropic fluid as a first model, where $q$ is a deceleration parameter. For the second model we assume viscous polytropic gas interacting with the scalar field. We investigate problem numerically and analyze behavior of different cosmological parameter concerning to components and behavior of Universe. We also compare our results with observational data to fix parameters of the models. We find some instabilities in the first model which may disappear in the second model for the appropriate parameters. Therefore, we can propose interacting quintessence dark energy with viscous polytropic gas as a successful model to describe Universe., Comment: 16 pages. Overlaps removed and References added

In this paper, we study the main cosmological properties of the classical Friedmann equations in the case of homogeneous and isotropic Friedmann-Robertson-Walker Universe and we also generalized the expression of the Friedmann equation in the case of Loop Quantum Cosmology (LQC). Considering the $M_{35}$-model, we found the solutions of the equations considered for two particular cases, i.e. $Q=0$ (i.e., the de Sitter solution) and $Q>0$. Moreover, we considered and studied two exact cosmological solutions of the $M_{35}$-model, in particular the power-law and the exponential ones. Futhermore, we also considered a third more complicated case and we derived the solution for an arbitrary function of the time $f\left(t\right)$. A scalar field description of the model is presented by constructing its self-interacting potential., Comment: arXiv admin note: text overlap with arXiv:1107.1558 by other authors

The subject of this paper is to investigate the weak regime covariant scalar-tensor-vector gravity (STVG) theory, known as the MOdified gravity (MOG) theory of gravity. First, we show that the MOG in the absence of scalar fields is converted into $\Lambda(t),G(t)$ models. Time evolution of the cosmological parameters for a family of viable models have been investigated. Numerical results with the cosmological data have been adjusted. We've introduced a model for dark energy (DE) density and cosmological constant which involves first order derivatives of Hubble parameter. To extend this model, correction terms including the gravitational constant are added. In our scenario, the cosmological constant is a function of time. To complete the model,interaction terms between dark energy and dark matter (DM) manually entered in phenomenological form. Instead of using the dust model for DM, we have proposed DM equivalent to a barotropic fluid. Time evolution of DM is a function of other cosmological parameters. Using sophisticated algorithms, the behavior of various quantities including the densities, Hubble parameter, etc. have been investigated graphically. The statefinder parameters have been used for the classification of DE models. Consistency of the numerical results with experimental data of $SneIa+BAO+CMB$ are studied by numerical analysis with high accuracy., Comment: A version accepted for publication in "International Journal of Theoretical Physics"

In this paper we consider a universe filled with barotropic dark matter and Ricci dark energy in Lyra geometry with varying Lambda. We assume two different kinds of interactions between dark matter and dark energy. Then, by using numerical analysis, we investigate some cosmological parameters of the models such as equation of state, Hubble and deceleration parameters., Comment: 14 pages

In this paper, we consider three different models of dark energy in higher dimensional space-time and discuss about some cosmological parameters numerically. The first model is a single component universe including viscous varying modified Chaplygin gas. In the second model, we consider two-component universe including viscous varying modified Chaplygin gas and ghost dark energy. In the third model, we consider another two-component universe including viscous modified cosmic Chaplygin gas and ghost dark energy. In the cases of two-component fluids we also consider possibility of interaction between components.

In this paper, we study two different models of dark energy based on Chaplygin gas equation of state. The first model is the variable modified Chaplygin gas while the second one is the extended Chaplygin gas. Both models are considered in the framework of higher order $f(R)$ modified gravity. We also consider the case of time varying gravitational constant $G$ and $\Lambda$ for both models. We investigate some cosmological parameters such as the Hubble, the deceleration and the equation of state parameters. Then we showed that the model that we considered, extended Chaplygin gas with time-dependent $G$ and $\Lambda$, is consistent with the observational data. Finally we conclude with the discussion of cosmological perturbations of our model., Comment: Perturbation analysis added, typos corrected, references added

In this paper we consider two models of quintessence scalar fields with different potentials. Interaction with generalized cosmic Chaplygin gas is also investigated. Cosmological parameters are studied and graphical behavior is analyzed. We find that our model is agree with observational data specially $\Lambda$CDM model., Comment: 8 pages, accepted in Int. J. Theor. Phys

In this paper, we study quintessence cosmology with an effective $\Lambda$-term in Lyra manifold. We consider three different models by choosing variable $\Lambda$ depend on time, the Hubble parameter and the energy density of dark matter and dark energy. Dark energy assumed as quintessence which interacts with the dark matter. By using numerical analysis we investigate behavior of cosmological parameters in three different models and compare our results with observational data. Statefinder diagnostic is also performed for all models., Comment: 10 pages

We investigate interacting ghost dark energy models in higher dimensional cosmology. We attempt to model dark matter within a barotropic fluid with $P_{b}=\omega(t)_{b}\rho$. In this work we consider four different models based on choosing equation of state parameter and interaction term. We confirm that our models agree with observational data., Comment: 13 pages, 6 figures. arXiv admin note: text overlap with arXiv:1308.3450

In this paper, we study three models of f(R) modified gravity including higher order terms based on different equation of state parameter. We also assume variable G and $\Lambda$. By using numerical analysis, we obtain the behavior of some important cosmological parameters, like the Hubble expansion H parameter and the deceleration parameter q. The statefinder diagnostics is also performed for all models., Comment: Accepted in Can. J. Phys

We consider a model of the Universe with variable G and {\Lambda}. Subject of our interest is a phenomenological model for {\Lambda} proposed and considered in this article first time (up to our knowledge). Modification based on an assumption that ghost dark energy exists and Universe will feel it through {\Lambda}. In that case we would like to consider possibility that there exist some unusual connections between different components of the fluids existing in Universe. We would like to stress, that this is just an assumption and could be very far from the reality. We are interested by this model as a phenomenological and mathematical and unfortunately, we will not discuss about physical conditions and possibilities of having such modifications. To test our assumption and to observe behavior of the Universe, we will consider toy models filled by a barotropic fluid and modified Chaplyagin gas. To complete the logic of the research we will consider interaction between barotropic fluid or Chaplygin gas with ghost dark energy as a separate scenario. Statefinder diagnostic also provided with stability analysis of the models. All free parameters of the model fixed to satisfy generalized second law of thermodynamics., Comment: 13 pages

In this paper, we consider Universe filled with two-component fluid. We study two different models. In the first model we assume barotropic fluid with the linear equation of state as the first component of total fluid. In the second model we assume Van der Waals gas as the first component of total fluid. In both models, the second component assumed generalized ghost dark energy. We consider also interaction between component and discuss, numerically, cosmological quantities for two different parametrization of EoS which varies with time. We consider this as a toy model of our Universe. We fix parameters of the model by using generalized second law of thermodynamics. Comparing our results with some observational data suggests interacting barotropic fluid with EoS parameter $\omega(t)=\omega_{0}\cos(tH)+\omega_{1}t\frac{\dot{H}}{H}$ and generalized ghost dark energy as an appropriate model to describe our Universe., Comment: 11 page, accepted in Int. J. of Geometric Methods in Modern Physics

In this article we will consider several phenomenological models for the Universe with varying $G$ and $\Lambda(t)$, where $G$ is the gravitational "constant" and $\Lambda(t)$ is a varying cosmological "constant". Two-component fluid model taken into account. An interaction of the phenomenological form between a barotropic fluid and a quintessence DE is supposed. Three different forms of $\Lambda(t)$ will be considered. The problem is analysed numerically and behavior of different cosmological parameters investigated graphically. Conclusion and discussions are given at the end of the work. In an Appendix an information concerning to the other cosmological parameters is presented., Comment: 19 pages. revisited according to the comments of referees. arXiv admin note: text overlap with arXiv:astro-ph/0004125, arXiv:1304.1961 by other authors

In this paper we make steps in a new direction by considering fluids with EoS of more general form $F(\rho,P)=0$. It is thought that there should be interaction between cosmic fluids, but this assumption for this stage carries only phenomenological character opening a room for different kind of manipulations. In this article we will consider a modification of an interaction $Q$, where we accept that interaction parameter $b_{1}$ (order of unity) in $Q=3Hb_{1}\rho$ is time dependent and presented as a linear function of Hubble parameter $H$ of the form $b_{0}+btH$, where $b$ and $b_{0}$ are constants. We consider two different models include modified Chaplygin gas and palotropic gas which have bulk viscosity. Then, we investigate problem numerically and analyze behavior of different cosmological parameters concerning to fluids and behavior of Universe., Comment: 21 pages. Comparison with observational data added in new version

In this paper we consider Tachyonic scalar field as dark energy with interaction between components in the case of variable $G$ and $\Lambda$. We assume a flat Universe with specific form of scale factor and study cosmological parameters numerically and graphically. Statefinder analysis also performed as well. In the special choice of interaction parameters we succeed to obtain analytical expression of densities. We find that our model will be stable in the late stage but there is an instability at the early Universe., Comment: 17 pages, accepted by Research in Astronomy and Astrophysics (RAA). arXiv admin note: text overlap with arXiv:1402.2592 by other authors

In this paper we are interested to consider mathematical ways to obtain different phenomenological fluids from two-component Tachyonic scalar fields. We consider interaction between components and investigate problem numerically. Statefinder diagnostics and validity of the generalized second law of thermodynamics performed and checked. We suppose that our Universe bounded by Hubble horizon., Comment: 12 pages

In this paper we consider several phenomenological models of variable $\Lambda$. Model of a flat Universe with variable $\Lambda$ and $G$ is accepted. It is well known, that varying $G$ and $\Lambda$ gives rise to modified field equations and modified conservation laws, which gives rise to many different manipulations and assumptions in literature. We will consider two component fluid, which parameters will enter to $\Lambda$. Interaction between fluids with energy densities $\rho_{1}$ and $\rho_{2}$ assumed as $Q=3Hb(\rho_{1}+\rho_{2})$. We have numerical analyze of important cosmological parameters like EoS parameter of the composed fluid and deceleration parameter $q$ of the model., Comment: 20 pages, 21 figures. arXiv admin note: substantial text overlap with arXiv:1308.1819

This article motivated by the recent articles and results of two authors. Recently, J. Sadeghi and H. Farahani presented a work [1], where they include viscosity and analyze general model, by this way they extended models considered by M. Khurshudyan [2] and [3]. In this article, We tempt to consider varying Modified Chaplygin gas model in case of variable $G$ and $\Lambda$. It is well known, that varying $G$ and $\Lambda$ gives rise to modified field equations and modified conservation laws. We will consider two different toy models. First model is a Universe with one component phenomenological gas of our consideration, while for the second model we assume existence of a composed fluid of gas and a matter with $P=\omega(t)\rho_{m}$. Sign changeable interaction between fluids is accepted. We will analyze important cosmological parameters like EoS parameter of a fluid, deceleration parameter $q$ of the model., Comment: 16 pages, 12 figure

In this paper, we consider an unusual connection between different fluids. Having established a research goal we would like to consider a toy model of the Universe and investigate its behavior, especially for later time evolution for well known facts. The main goal of the article is to consider a toy model of the Universe with generalized ghost dark energy, Van der Waals gas and a phenomenologically modified fluid. The origin of the last component can be understood as a result of interaction between some original fluid and some source of energy or matter in Universe. By unusual connection we mean an assumption that generalized ghost dark energy has its contribution to the model by an interaction term $Q$ and we suppose an interaction of the form $Q=3Hb(\rho_{\small{tot}}-\rho_{GDe})$. Graphical analysis is performed and the questions of validity of the generalized second law of thermodynamics and stability of the model also approached in this paper.