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In this work, we investigate cosmological perturbations of viscous modified chaplygin gas model. Using $1+3$ covariant formalism, we define covariant and gauge invariant gradient variables, which after the application of scalar decomposition and harmonic decomposition techniques together with redshift transformation method, provide the energy overdensity perturbation equations in redshift space, responsible for large-scale structure formation. In order to analyze the effect of the viscous modified chaplygin gas model on matter overdensity contrast, we numerically solve the perturbation equations in both long and short wavelength limits. The numerical results show that the energy overdensity contrast decays with redshift. However, the perturbations which include amplitude effects due to the viscous modified chaplygin model do differ remarkably from those in the $\mathrm{\Lambda }$CDM. In the absence of viscous modified chaplygin model, the results reduce to those of $\mathrm{\Lambda }$CDM.

In this study, we construct a theoretical framework based on the generalized Hubble parameter form which may arise within the particle creation, viscous and $f(R)$ gravity theory. The Hubble parameter is scrutinized for its compatibility with the observational data relevant to the late-time universe. By using Bayesian statistical techniques based on ${\chi }^2$ minimization method, we determine model parameters’ best fit values for the cosmic chronometer and supernovae Pantheon datasets. For the best fit values, the cosmographic and physical parameters are analyzed to understand the cosmic dynamics in model. We also analyze the model section criterion in comparison to the $\mathrm{\Lambda }$ cold dark matter model.

A coupled double-distribution-function (DDF) lattice Boltzmann method was recently developed for the compressible Navier–Stokes equations. In this method, the specific-heat ratio and the Prandtl number can be easily adjusted. However, the ratio between the bulk and shear viscosities is fixed at a value related to the specific-heat ratio. In order to obtain a bulk viscosity satisfying the Stokes' hypothesis or an adjustable bulk viscosity in the recovered momentum and energy equations, correction terms, which are proportional to the divergence of macroscopic velocity, are incorporated into the microscopic evolution equations. The constraints imposed on these correction terms can be derived from the Chapman–Enskog analysis. With these constraints, the forms of the correction terms can be determined, and then a coupled DDF lattice Boltzmann model with adjustable specific-heat ratio, Prandtl number, and bulk viscosity can be obtained. Numerical simulations are performed for the attenuation of sound waves. The numerical results are found to be in good agreement with the theoretical solutions.

We present a discussion of the effects induced by the bulk viscosity on the very early Universe stability. The matter filling the cosmological (isotropic and homogeneous) background is described by a viscous fluid having an ultrarelativistic equation of state and whose viscosity coefficient is related to the energy density via a power-law of the form ζ = ζ₀ ρ^ν. The analytic expression of the density contrast (obtained for ν = 1/2) shows that, for small values of the constant ζ₀, its behavior is not significantly different from the non-viscous one derived by Lifshitz. But as soon as ζ₀ overcomes a critical value, the growth of the density contrast is suppressed forward in time by the viscosity and the stability of the Universe is favored in the expanding picture. On the other hand, in such a regime, the asymptotic approach to the initial singularity (taken at t = 0) is deeply modified by the apparency of significant viscosity in the primordial thermal bath, i.e. the isotropic and homogeneous Universe admits an unstable collapsing picture. In our model this feature also regards scalar perturbations while in the non-viscous case it appears only for tensor modes.

In this paper we calculate the thermodynamic quantities and bulk viscosity in a simple confining Dyson–Schwinger equation model of two-flavor QCD. Our results show that the velocity of sound shows a sharp increase around and at the phase transition temperature the derivative of the velocity with respect to T has a distinct change. It is also found that the trace anomaly increases sharply below the phase transition point and the bulk viscosity has a peak located at which is almost the same as the peak of the trace anomaly. A comparison of our results with those in the previous literature is given.

In this paper, based on Kubo's formula and the QCD low energy theorem, we propose a direct formula for calculating the bulk viscosity of QCD at finite chemical potential μ and zero temperature. According to this formula, the bulk viscosity at finite μ is totally determined by the dressed quark propagator at finite μ. We then use a dynamical, confining Dyson–Schwinger equation model of QCD to calculate the bulk viscosity at finite μ. It is found that no sharp peak behavior of the bulk viscosity at finite μ is observed, which is quite different from that of the bulk viscosity at finite temperature.

We study the effect of magnetic field on the transport properties like shear and bulk viscosities of hot and dense hadronic matter within hadron resonance gas model. We estimate the bulk viscosity using low energy theorems for bilocal correlators of the energy–momentum tensor generalized to finite temperature, density and magnetic field. We use Gaussian ansatz for the spectral function at low frequency. We estimate shear viscosity coefficient using molecular kinetic theory. We find that vacuum contribution due to finite magnetic field dominates the bulk viscosity (ζ) for the temperatures up to 0.1 GeV and increases with magnetic field while ratio ζ/s decreases with magnetic field. We also find that shear viscosity coefficient of hadronic matter decreases with magnetic field.

A universe media is considered as a bulk viscosity described by inhomogeneous equation of state (EOS) of the form $p=(\gamma -1)\rho +\Lambda (t)$, where $\Lambda (t)$ is a time-dependent parameter. A generalized dynamical equation for the scale factor of the universe is proposed to describe the cosmological evolution, in which we assume the bulk viscosity and time-dependent parameter $\Lambda$ are linear combination of two terms of the form: $\zeta ={\zeta }_0+{\zeta }_{1}H$ and $\Lambda (t)={\Lambda }_0+{\Lambda }_{1}H$, i.e.one is constant and other is proportional to Hubble parameter $H=\frac{ȧ}{a}$. In this framework, we demonstrate that this model can be used to explain the dark energy dominated universe, and the inhomogeneous term of specific form introduced in EOS, may lead to three kinds of fates of cosmological evolution: no future singularity, big rip or TypeIII singularity as presented by [S. Nojiri and S. D. Odintsov, Phys. Rev. D72, 023003 (2005)].

We have gone through a comparative study on two different kinds of bulk viscosity expressions by using a common dynamical model. The Polyakov–Nambu–Jona-Lasinio (PNJL) model in the realm of mean-field approximation, including up to eight quark interactions for 2+1 flavor quark matter, is treated for this common dynamics. We have probed the numerical equivalence as well as discrepancy of two different expressions for bulk viscosity at vanishing quark chemical potential. Our estimation of bulk viscosity to entropy density ratio follows a decreasing trend with temperature, which is observed in most of the earlier investigations. We have also extended our estimation for finite values of quark chemical potential.

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 motivation of this paper is to study the bulk viscosity effect in Ricci dark energy (RDE) model within the framework of modified f(R, T) gravity, where R is the Ricci scalar and T is the trace of the energy–momentum tensor. As most studies assume that the universe is filled with a perfect fluid, viscosity is expected to present at least during some stages, especially in the early stage of the evolution of the universe but it could still become significant in the future. We assume the universe is filled with viscous RDE and pressureless dark matter. We consider the total bulk viscous coefficient is in the form of $\zeta ={\zeta }_0+{\zeta }_1$H, where ${\zeta }_0$ and ${\zeta }_1$ are the constants. We obtain the solutions to the modified field equations by assuming a form f(R, T) = R$+\lambda$T, where $\lambda$ is a constant. We find the scale factor and deceleration parameter, and classify all possible evolutions of the universe. We briefly discuss the future finite-time singularity and show that the Big Rip singularity appears in viscous RDE model. We investigate two geometrical diagnostics, statefinder parameter and Om to analyze the dynamics of evolution of the universe. The trajectories of statefinder parameter reveal that the model behaves like quintessence for small $\zeta$, and for large $\zeta$ it shows the Chaplygin gas-like. However, in late time both the models approach $\mathrm{\Lambda }$CDM. The model shows a transition from decelerated phase to accelerated phase. Similarly, the Om analysis reveals that the model behaves like quintessence for small $\zeta$ and phantom-like for large $\zeta$. We extend our study to analyze the time evolution of the total entropy and generalized second law of thermodynamics of viscous RDE model in f(R, T) theory inside the apparent horizon. Our study shows that the generalized second law of thermodynamics always preserves in viscous RDE model in a region enclosed by the apparent horizon under the suitable constraints of viscous coefficients.

Bulk viscosity is an important transport coefficient that exists in the hydrodynamical limit only when the underlying theory is non-conformal. One example being thermal QCD with large number of colors. We study bulk viscosity in such a theory at low energies and at weak and strong ’t Hooft couplings when the temperature is above the deconfinement temperature. The weak coupling analysis is based on Boltzmann equation from kinetic theory whereas the strong coupling analysis uses non-conformal holographic techniques from string and M-theories. Using these, many properties associated with bulk viscosity may be explicitly derived.

Considering the modified viscous Chaplygin gas as the form of dark energy contained in the Universe, we study the interaction of dark energy with other components like electromagnetic field comprising the Universe. It is incidentally found that the interaction effect behaves like the electric charge from an electromagnetic field showing the possibility that a part of the dark energy can be utilized in the form of electrical energy. Further, from studying geometrical and physical behaviors of the evolution of this model Universe, it can be rightly said that this derived model behaves as the actual Universe.

We introduce a time-delay function in bulk viscosity cosmology. Even for bulk viscosity functions where closed-form solutions are known, because of the time-delay term, the exact solutions are lost. Therefore in order to study the cosmological evolution of the resulting models we perform a detailed analysis of the stability of the critical points, which describe de Sitter solutions, by using Lindstedt’s method. We find that for the stability of the critical points it depends also on the time-delay parameter, where a critical time-delay value is found which plays the role of a bifurcation point. For time-delay values near the critical value, the cosmological evolution has a periodic evolution, this oscillating behavior is because of the time-delay function. We find a new behavior near the exponential expansion point, which can be seen also as an alternative way to exit the exponential inflation.

New agegraphic dark energy (NADE) model with bulk viscosity is proposed by assuming that the universe is composed of the NADE and dark matter, and both the dark components have a bulk viscosity. At the matter-dominated epoch, the density parameter and the equation of state (EoS) of the viscous NADE are given by ${\mathrm{\Omega }}_q={(1-9{\tau }_m)}^2{n}^2{(1+z)}^{-2}∕4$ and $w_q=-2∕3+3({\tau }_q-{\tau }_m)$, respectively, where ${\tau }_q$ and ${\tau }_m$ are viscosity parameters. In the late time $z\to -1$, the NADE dominates ${\mathrm{\Omega }}_q\to 1$ and $w_q\to -1+3{\tau }_q$. Owing to the special analytic features at the matter-dominated epoch for the viscous NADE model, the initial condition ${\mathrm{\Omega }}_q(z_{\mathrm{\text{ini}}})={(1-9{\tau }_m)}^2{n}^2{(1+z_{\mathrm{\text{ini}}})}^{-2}∕4$ at $z_{\mathrm{\text{ini}}}=2000$ is used to solve the differential equation of ${\mathrm{\Omega }}_q$, and the other physical quantities can be obtained correspondingly. We also find that the viscosity of dark matter affects the current density and the start time of the cosmic acceleration. However, in the late time $w_q$ only depends on the viscosity of the dark energy. Furthermore, we investigate the viscous NADE model by means of statefinder diagnostic. The viscosity of dark matter significantly affects the evolution of the statefinder parameters. Therefore, the bulk viscosity plays a significant role in the cosmological evolution.

This study investigates the dynamics of a spatially homogeneous and anisotropic LRS Bianchi type-I Universe with viscous fluid in the framework of $f(Q)$ symmetric teleparallel gravity. We assume a linear form for $f(Q)$ and introduce hypotheses regarding the relationship between the expansion and shear scalars, as well as the Hubble parameter and bulk viscous coefficient. The model is constrained using three observational datasets: the Hubble dataset (31 data points), the Pantheon SN dataset (1048 data points), and the BAO dataset (6 data points). The calculated cosmological parameters indicate expected behavior for matter-energy density and bulk viscous pressure, supporting the universe’s accelerating expansion. Diagnostic tests suggest that the model aligns with a $\mathrm{\Lambda }$CDM model in the far future and resides in the quintessence region. These findings are consistent with recent observational data and contribute to our understanding of cosmic evolution within the context of modified gravity and bulk viscosity.

In this paper, we reconsider the concept of bulk viscosity in Brans–Dicke theory to study accelerated expansion of the universe in a flat Friedmann–Robertson–Walker metric. In recent works on bulk viscosity in Brans–Dicke theory, the power-law form of Brans–Dicke scalar field has been taken to explain recent phase transition of the universe, however, power-law form confronts constant deceleration parameter problem. Therefore, we consider recently proposed well-motivated logarithmic form of Brans–Dicke scalar field to discuss bulk viscous model in Brans–Dicke theory. We obtain the values of deceleration parameter and equation of state parameter for the model, and plot their graphs against the redshift parameter z. The plots show that the model is able to explain the recent phase transition of the universe and equation of state parameter shows the behavior of dark energy. Further, we apply two important analysis, namely, $w-w^{\prime }$ analysis and thermodynamic analysis to examine our model. The $w-w^{\prime }$ analysis shows that our model belong to thawing region and shows similarities with quintessence model. All the trajectories start from the point $w^{\prime }=0$ with different negative values of w having quintessence behavior. The thermodynamic analysis shows that the model satisfies generalized second law of thermodynamics.

Tilted Bianchi type-V barotropic fluid cosmological models with heat conduction and variable bulk viscosity is investigated. To get the deterministic model of the universe, we have assumed two conditions: (i) A = (BC)ⁿ and (ii) ζθ = const where A, B, C are metric potentials, n is a constant, ζ the coefficient of bulk viscosity, θ the expansion in the model. The behavior of the model in presence and absence of bulk viscosity and singularities in the model are discussed. Some thermodynamic relations and physical aspects of the model related to the observation on the present day universe are also discussed.

Based on the first principle calculation, a Lagrangian for the system describing quarks, gluons, and their interactions, is constructed. Ascribed to the existence of dissipative behavior as a consequence of strong interaction within quark–gluon plasma (QGP) matter, auxiliary terms describing viscosities are constituted into the Lagrangian. Through a "kind" of phase transition, gluon field is redefined as a scalar field with four-vector velocity inherently attached. Then, the Lagrangian is elaborated further to produce the energy–momentum tensor of dissipative fluid-like system and the equation of motion (EOM). By imposing the law of energy and momentum conservation, the values of shear and bulk viscosities are analytically calculated. Our result shows that, at the energy level close to hadronization, the bulk viscosity is bigger than shear viscosity. By making use of the conjectured values η/s~1/4π and ζ/s~1, the ratio of bulk to shear viscosity is found to be ζ/η>4π.

In this work, we have studied various cosmological parameters in the presence of viscous new Tsallis holographic dark energies for interacting scenarios in the framework of Chern–Simons modified gravity. The bulk viscosity has been considered with the bulk viscous pressure chosen in the form $\mathrm{\Pi }=-3H\left(\right.{\xi }_0+{\xi }_{1}H+{\xi }_2(Ḣ+H^2)\left)\right.$. Hubble parameter $H$ has been obtained from the above choice of scale factor and in this viscous scenario, the effective pressure has been obtained in Chern–Simons framework whose field equation, cosmological consequences have been investigated. It has been observed that for the interaction scenario in the presence of bulk viscosity the EoS parameter is staying above $-1$, which indicates quintessence behavior. Hence, for the universe filled with a bulk viscous fluid can have the possibility of avoidance of big-rip, although the earlier transition from quintessence to phantom is not avoidable.