Narrow Results

A one-component dark energy fluid model of the late universe is considered $(w<-1)$ when the fluid, initially assumed laminar, makes a transition into a turbulent state of motion. Spatial isotropy is assumed so that only the bulk viscosities are included ($\zeta$ in the laminar epoch and ${\zeta }_{\mathrm{\text{turb}}}$ in the turbulent epoch). Both viscosities are assumed to be constants. We derive a formula, new as far as we know, for the time dependence of the temperature $T(t)$ in the laminar case when viscosity is included. Assuming that the laminar/turbulent transition takes place at some time $t_s$ before the big rip is reached, we then analyze the positive temperature jump experienced by the fluid at $t=t_{\ast }$ if ${\zeta }_{\mathrm{\text{turb}}}>\zeta$. This is just as one would expect physically. The corresponding entropy production is also considered. A special point emphasized in the paper is the analogy that exists between the cosmic fluid and a so-called Maxwell fluid in viscoelasticity.

We analyze characteristic properties of two different cosmological models: (i) a one-component dark energy model where the bulk viscosity $\zeta$ is associated with the fluid as a whole, and (ii) a two-component model where $\zeta$ is associated with a dark matter component ${\rho }_{\mathrm{\text{m}}}$ only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation-of-state $p=w\rho$ with $w$ a constant. In the one-component model, we consider two possibilities, either to take $\zeta$ proportional to the scalar expansion (equivalent to the Hubble parameter), in which case the evolution becomes critically dependent on the value of the small constant $\alpha =1+w$ and the magnitude of $\zeta$, or we consider the case $\zeta =\mathrm{\text{const.}}$, where a de Sitter final stage is reached in the future. In the two-component model, we consider only the case where the dark matter viscosity ${\zeta }_{\mathrm{\text{m}}}$ is proportional to the square of ${\rho }_{\mathrm{\text{m}}}$, where again a de Sitter form is found in the future. In this latter case, the formalism is supplemented by a phase space analysis. As a general result of our considerations, we suggest that a value ${\zeta }_0\sim 10^6\mathrm{\text{Pa}}\cdot \mathrm{\text{s}}$ for the present viscosity is reasonable, and that the two-component model seems to be favored.

The illustration of cosmic acceleration is being presented in the framework of DGP braneworld and dynamical Chern–Simons modified gravity in the presence of casual Israel–Stewart formalism. In this way, we discuss the evolution parameter which leads to the accelerated expansion of the universe in the phantom as well as quintessence region for both gravities. The squared speed of sound $\left({v_s}^2\right)$ leads to the stable behavior of the current physical system in both gravities in the later epoch. Also, the entropy variation, as well as thermal equilibrium condition, remains valid in both frameworks at the present and later epoch.

The cosmological model executing hybrid expansion law (HEL) of scale factor in Randall–Sundrum type II (RS) braneworld gravity with Gauss–Bonnet terms in the presence of bulk viscosity described by Eckart theory, Truncated Israel–Stewart (TIS) theory, Full Israel–Stewart (FIS) theory and nonlinear Israel–Stewart (nIS) theory is studied. In the hybrid expansion law, the scale factor of the universe is described by the product of power-law and exponential expansions. In the HEL model, the early inflation and its transition from deceleration phase to present accelerated phase of expansion can be explored. The constraints of hybrid expansion law model parameters are determined using the recent observational data. Thereafter, the estimated parameters are considered to explore the present value of deceleration parameter, jerk parameter and transition epoch from early deceleration to the present accelerating phase.

The holographic principle in a radiation dominated universe is extended to incorporate the case of a bulk-viscous cosmic fluid. This corresponds to a nonconformally invariant theory. Generalization of the Cardy-Verlinde entropy formula to the viscous case appears to be possible from a formal point of view, although we question on physical grounds the manner in which the Casimir energy is evaluated in this case. Also, we consider in the present paper an observation recently made by Youm, namely that the entropy of the universe is no longer expressible in the conventional Cardy-Verlinde form if one relaxes the radiation dominance equation of state and instead merely assumes that the pressure is proportional to the energy density. We show that Youm's generalized entropy formula remains valid when the cosmic fluid is no longer ideal, but endowed with a constant bulk viscosity ζ.

We discuss a modified form of gravity implying that the action contains a power α of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for a general α. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2α-1) of the scalar expansion. In Einstein's gravity, where α = 1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the authors, there exists in principle a viscosity-driven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.

We consider a modified form of gravity in which the action contains a power α of the scalar curvature. It is shown how the presence of a bulk viscosity in a spatially flat universe may drive the cosmic fluid into the phantom region (w < -1) and thus into a Big Rip singularity, even if it lies in the quintessence region (w > -1) in the nonviscous case. The condition for this to occur is that the bulk viscosity contains the power (2α-1) of the scalar expansion. Two specific examples are discussed in detail. The present paper is a generalization of the recent investigation dealing with barrier crossing in Einstein's gravity: I. Brevik and O. Gorbunova, Gen. Relativ. Gravit.37, 2039 (2005).

In this paper, we investigate the viscous modified Chaplygin gas cosmological model. Solutions for different values of the viscosity parameter are obtained using both analytical and numerical methods. We have calculated the deceleration and defined newly statefinder {r, s} pair in D dimensions. It is shown that when D = 4, the usual statefinder parameters are recovered. Furthermore, we apply the statefinder diagnostic to the MCG model with and without viscosity in D dimensions and explore these parameters graphically.

From a hydrodynamicist’s point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (exluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review, we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we study viscous cosmology in the late universe, containing current acceleration and the possible future singularities, and we investigate how one may even unify inflationary and late-time acceleration. Finally, we analyze the viscosity-induced crossing through the quintessence-phantom divide, we examine the realization of viscosity-driven cosmological bounces, and we briefly discuss how the Cardy–Verlinde formula is affected by viscosity.

We analyze gravitational waves propagating in an isotropic cosmic fluid endowed with a bulk viscosity $\zeta$ and a shear viscosity $\eta$, assuming these coefficients to vary with fluid density $\rho$ as ${\rho }^{\lambda }$, with $\lambda =1/2$ favored by experimental evidence. We give the general governing equation for the gravitational waves and focus thereafter on two examples. The first concerns waves in the very late universe, close to the Big Rip, where the fate of the cosmic fluid is dependent highly on the values of the parameters. Our second example considers the very early universe, the lepton era, the motivation for this choice being that the microscopical bulk viscosity as calculated from statistical mechanics is then at maximum. We find that the gravitational waves on such an underlying medium are damped, having a decay constant equal to the inverse of the conformal Hubble parameter. Our results turn out to be in good agreement with other viscosity-based approaches.

We describe the evolution of the early and late universe from thermodynamic considerations, using the generalized nonextensive Tsallis entropy with a variable exponent. A new element in our analysis is the inclusion of a bulk viscosity in the description of the cosmic fluid. Using the generalized Friedmann equation, a description of the early and the late universe is obtained.

We propose to describe the acceleration of the universe by introducing a model of two coupled fluids. We focus on the accelerated expansion at the early stages. The inflationary expansion is described in terms of a van der Waals equation of state for the cosmic fluid, when account is taken of bulk viscosity. We assume that there is a weak interaction between the van der Waals fluid and the second component (matter). The gravitational equations for the energy densities of the two components are solved for a homogeneous and isotropic Friedmann–Robertson–Walker (FRW) universe, and analytic expressions for the Hubble parameter are obtained. The slow-roll parameters, the spectral index, and the tensor-to-scalar ratio are calculated and compared with the most recent astronomical data from the Planck satellite. Given reasonable restriction on the parameters, the agreement with observations is favorable.

We describe the accelerated expansion of the late-time universe using a generalized equation of state (EoS) when account is taken of bulk viscosity. We assume a homogeneous and isotropic Friedmann–Robertson–Walker spacetime. Solutions of the gravitational equations for dark energy are obtained in implicit form. Characteristic properties of the universe evolution in the presence of the viscosity effects are discussed. Finally, the dynamics of the accelerated expansion of the viscous universe are discussed on the basis of a modified logarithmic-corrected EoS.

We investigate bounce cosmological models in the presence of a viscous fluid, making use of generalized holographic cutoffs introduced by Nojiri and Odintsov [Covariant generalized holographic dark energy and accelerated universe, Eur. Phys. J. C77 (2017) 528, arXiv:1703.06372 [hep-th]]. We consider both an exponential, a power-law, and a double exponential form for the scale factor. By use of these models, we calculate expressions for infrared cutoffs analytically, such that they correspond to the particle horizon at the bounce. Finally, we derive the energy conservation equation, from the holographic point of view. In that way, the relationship between the viscous fluid bounce and the holographic bounce is demonstrated.

This paper is devoted to the application of the holographic principle to describe Rip brane cosmological models in the presence of a bulk viscosity. We make use of the generalized infrared-cutoff holographic dark energy, introduced by Nojiri and Odintsov. We consider various examples: Rip brane cosmology corresponding to the Little Rip case, asymptotic de Sitter theory, and the so-called Big Freeze theory leading to a singularity. Analytical expressions for infrared cutoffs, as well as the particle and the future horizons at the brane, are obtained. The equations for energy conservation on the brane within the holographic theory are obtained in each case. The correspondence between viscous cosmology and holographic cosmology on the brane is shown.

In this paper, we consider a class of cosmological fluids that possess properties analogous to those of crystalline solids undergoing isotropic deformations. Our research is based on a modified log-corrected power-law equation of state in the presence of a bulk viscosity. This formalism represents a class of the so-called logotropic fluids, and allows explaining an accelerating late-time universe. 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 to dark matter, and study various interacting forms between them. We solve the system of equations for a modified log-power-law fluid coupled to dark matter, and obtain expressions for the log-corrected power-law energy density, and the energy density for dark matter. A comparative analysis is made with the model of a nonviscous log-corrected power-law fluid without interaction with dark matter.

In this paper, we apply the holographic principle for describing in a unifying way the early and the late-time universe, when the general equation of state contains a bulk viscosity. We use the idea of a generalized cut-off holographic dark energy introduced by Nojiri and Odintsov (2006, 2017), and study the evolution of the universe when the equation of state has two power-law asymptotes. Analytical expressions for the infrared cut-offs in terms of the particle horizon are obtained. The energy conservation laws as derived from the holographic point of view, are given for various forms of the thermodynamic parameters and for various forms of the bulk viscosity. As a result, we obtain a unifying description of the early and the late-time universe in the presence of a viscous holographic fluid.