Alexander V. Timoshkin

We apply the holographic principle based on the generalized infrared cut-off introduced by Nojiri-Odintsov [1, 2] for describing cosmological models of the universe induced by a viscous fluid in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) metric. We study the evolution of the universe in terms of the generalized equation of state (EoS) parameters. We consider the early universe, including the bounce cosmology, the inflation, and the model of the unified early and late universe. Finally, we derive the energy conservation equation from the holographic point of view in terms of generalized infrared cut-offs. As a result, we obtain an equivalent description of the bounce, inflation, unified early and late-time universe, in terms of a viscous fluid and holographic fluid.

In this paper, the application of entropy cosmology in describing cosmic inflation is investigated. Our research is based on a new multi-parameter generalized entropy, which can generalize all the known entropies proposed so far, for suitable representations of the entropic parameters. We investigated a cosmological model of an inflationary universe under a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric by using different forms of thermodynamic parameters and bulk viscosity in the Equation of State (EoS). We employ the holographic description based on generalized infrared cut-off proposed by Nojiri and Odintsov to solve the equations of motion for gravity, and calculate the scale factor and the infrared cut-off with the future or particle horizon as parameters. The representation of the energy conservation from the holographic point of view is obtained. The corrections in the energy conservation equation related to the multi-parameter generalized entropy function allow creating more detailed picture of the evolution of the universe. Finally, the correspondence between spectral indices, tensor-to-scalar ratio, and the recent astronomical observation data from the Planck satellite is also discussed.

Some relevant aspects of a new form of generalized entropic cosmology, recently introduced by Nojiri, Odintsov and Faraoni, are considered. The setup is a logarithmic equation of state for a viscous dark fluid coupled with dark matter, in the ordinary Friedmann–Lemaître–Robertson–Walker flat universe. The influence of thermal effects, caused by Hawking radiation, near the singularity, are carefully investigated. In particular, their role on the formation and specific type of the Big Rip expected to occur within a finite time. It is shown that a scenario arises, where a qualitative change towards the good direction, in the type of the singularity formed, does occur. On top of that, another very interesting scenario is obtained, where the singularity vanishes completely.

The cosmological application of a dark viscous fluid in a spatially flat Friedmann-Robertson-Walker (FRW) universe with a modified logarithmic equation of state (EoS), being an analogue of the equation associated with the isotropic deformation of crystalline solids, is explored. This formalism represents a class of the so-called logotropic fluids, and allows explaining an accelerating late-time universe. Our research is based on a new generalized entropy function proposed by Nojiri-Odintsov-Faraoni [1]. We consider entropic cosmology and describe the evolution of the late time universe in the presence of dark matter coupled with viscous dark energy. In order to obtain a more detailed picture of its evolution, we add in our model a coupling of the log-corrected power-law fluid with dark matter, and study various interacting forms between them. We solve the system of dynamic equations for viscous dark fluid coupled with dark matter and obtain expressions for the log-corrected power-law dark energy density, and the energy density for dark matter. The research results are presented in holographic form in terms of generalized holographic cut-offs introduced by Nojiri and Odintsov [2, 3]. In the asymptotic case an expression for the Hubble function, and the energy density for dark matter in the entropic cosmology, are obtained.

Interest on the possible future scenarios the universe could have has grew substantially with breakthroughs on late-time acceleration. Holographic dark energy (HDE) presents a very interesting approach towards addressing late-time acceleration, presenting an intriguing interface of ideas from quantum gravity and cosmology. In this work we present an extensive discussion of possible late-time scenarios, focusing on rips and similar events, in a universe with holographic dark energy. We discuss these events in the realm of the generalized Nojiri–Odintsov cutoff and also for the more primitive holographic cutoffs like Hubble, particle and event horizon cutoffs. We also discuss the validity of the generalized second law of thermodynamics and various energy conditions in these regimes. Our work points towards the idea that it is not possible to have alternatives of the big rip consistently in the simpler HDE cutoffs, and shows the flexibility of the generalized HDE cutoff as well.

Bounce cosmological models containing a dark viscous fluid in a spatially flat Friedmann-Robertson-Walker (FRW) universe are considered. The universe evolution is described in terms of generalized equation of state (EoS) parameters, in presence of the bulk viscosity. Entropic cosmology plays a key role in the discussion, and the matter bounce behavior is described based on a non-singular, generalized entropy function, recently proposed by Odintsov and Paul. Three different forms for the scale factor are investigated: an exponential, a power-law, and a double-exponential function, respectively. Appropriate bounce cosmological models are formulated, via the relevant parameters of the modified EoS, and analytical expressions for the corresponding infrared cut-off are obtained, via the particle horizon. Results are displayed in holographic form, making use of generalized holographic cut-offs first introduced by Nojiri and Odintsov. In addition, the viability of the corresponding bounce cosmological models is investigated, taking into account the actual thermodynamic properties of our universe, by means of a no-singular, generalized entropy function. In the asymptotic case, an expression for the generalized entropy is obtained, which remarkably has the additivity property.

Interest on the possible future scenarios the universe could have has grew substantially with breakthroughs on late-time acceleration. Holographic dark energy (HDE) presents a very interesting approach towards addressing late-time acceleration, presenting an intriguing interface of ideas from quantum gravity and cosmology. In this work we present an extensive discussion of possible late-time scenarios, focusing on rips and similar events, in a universe with holographic dark energy. We discuss these events in the realm of the generalized Nojiri-Odintsov cutoff and also for the more primitive holographic cutoffs like Hubble, particle and event horizon cutoffs. We also discuss the validity of the generalized second law of thermodynamics and various energy conditions in these regimes. Our work points towards the idea that it is not possible to have alternatives of the big rip consistently in the simpler HDE cutoffs, and shows the flexibility of the generalized HDE cutoff as well.

Bounce cosmological models containing a dark viscous fluid in a spatially flat Friedmann–Robertson–Walker (FRW) universe are considered. The universe’s evolution is described in terms of generalized equation of state (EoS) parameters, in the presence of the bulk viscosity. Entropic cosmology plays a key role in the discussion, and the matter bounce behavior is described based on a nonsingular, generalized entropy function, recently proposed by S. D. Odintsov and T. Paul. Three different forms of the scale factor are investigated: an exponential, a power-law and a double-exponential function, respectively. Appropriate bounce cosmological models are formulated, via the relevant parameters of the modified EoS, and analytical expressions for the corresponding infrared cut-off are obtained, via the particle horizon. Results are displayed in holographic form, making use of generalized holographic cut-offs first introduced by S. Nojiri and S. D. Odintsov. In addition, the viability of the corresponding bounce cosmological models is investigated, taking into account the actual thermodynamic properties of our universe, by means of a no-singular, generalized entropy function. In the asymptotic case, an expression for the generalized entropy is obtained, which remarkably has the additivity property.

In this paper, we study Little Rip (LR) and Pseudo Rip (PR) cosmological models containing two coupled fluids: dark energy and dark matter. We assume a spatially flat Friedmann–Robertson–Walker (FRW) universe. The interaction between the dark energy and the dark matter fluid components is described in terms of the parameters in the generalized Equation of State (EoS) in presence of the bulk viscosity. We consider entropic cosmology and use a description based on a new generalized entropy function, which was proposed by Nojiri–Odintsov–Faraoni [From nonextensive statistics and black hole entropy to the holographic dark universe, Phys. Rev. D 105(4) (2022) 044042]. Conditions for the appearance of the (LR) and the (PR) in terms of the parameters of the (EoS) are obtained. Introducing an energy density [ ] corresponding to a specified entropy function [ ], together with an interaction term [ ] in the gravitational equations of motion, we derive modified forms of the EoS parameters. We discuss the corrections of the thermodynamic parameters associated with the generalized entropy function. Properties of the late universe as well as in the early universe in this formalism are pointed out.

Holographic principles have proven to be a very interesting approach towards dealing with the issues of the late-time acceleration of the universe, which has resulted in a great amount of work on holographic dark energy models. We consider one such very interesting holographic scenario, namely the Tsallis Holographic dark energy model, and consider an ansatz based approach to such models. We consider three cosmological scenarios in such models, namely those with viscous, non-viscous, and Chaplygin gas scenarios, discussing various crucial aspects related to these models. We discuss various crucial properties of the Tsallis model in such scenarios and see how the phantom divide is crossed in each case, but it is only the Chaplygin gas models which provide a better view on stability issues.The symmetry property of the theory presented in the article is the assumption that space is isotropic. Using bulk viscosity instead of shear viscosity reflects spatial isotropy.