The evolution of a flat, isotropic and homogeneous universe is studied. The background geometry in the early phases of the universe is conjectured to be filled with causal bulk viscous cosmological fluid and dark energy. The energy density relations obtained from the assumption of covariant conservation of energy-momentum tensor of the background matter in the early universe are used to derive the basic equation for the Hubble parameter $H$. The viscous properties described by ultra-relativistic equations of state and bulk viscosity taken from recent heavy-ion collisions and lattice QCD calculations have been utilized to give an approximate solution of the field equations. The cosmological constant is conjectured to be related to the energy density of the vacuum. In this treatment, there is a clear evidence for singularity at vanishing cosmic time $t$ indicating the dominant contribution from the dark energy. The time evolution of $H$ seems to last for much longer time than the ideal case, where both cosmological constant and viscosity coefficient are entirely vanishing.
We discuss influences of bulk viscosity on the Early Universe, which is modeled by Friedmann-Robertson-Walker metric and Einstein field equations. We assume that the matter filling the isotropic and homogeneous background is relativistic viscous characterized by ultra-relativistic equations of state deduced from recent lattice QCD simulations. We obtain a set of complicated differential equations, for which we suggest approximate solutions for Hubble parameter $H$. We find that finite viscosity in Eckart and Israel-Stewart fluids would significantly modify our picture about the Early Universe.
We consider the influence of the perturbative bulk viscosity on the evolution of the Hubble parameter in the QCD era of the early Universe. For the geometry of the Universe we assume the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker metric, while the background matter is assumed to be characterized by barotropic equations of state, obtained from recent lattice QCD simulations, and heavy--ion collisions, respectively. Taking into account a perturbative form for the bulk viscosity coefficient, we obtain the evolution of the Hubble parameter, and we compare it with its evolution f…
In this paper we have considered a flat FLRW universe with bulk viscous Zel'dovich as the cosmic component. Being considered the bulk viscosity as per the Eckart formalism, we have analyzed the evolution of the Hubble parameter and constrained the model with the Type Ia Supernovae data thus extracting the constant bulk viscous parameter and present Hubble parameter. Further we have analyzed the scale factor, equation of state and deceleration parameter. The model predicts the late time acceleration and is also compatible with the age of the universe as given by the oldest globular clusters. We…
Spatially homogeneous and anisotropic Bianchi type V space-time with bulk viscous fluid source and time varying gravitational constant $G$ and cosmological term $Λ$ are considered. Coefficient of bulk viscosity $ζ$ is assumed as a simple linear function of Hubble parameter $H$ (i.e. $ζ=ζ_0+ζ_1 H$, where $ζ_0$ and $ζ_1$ are constants). The Einstein field equations are solved explicitly by using a law of variation for the Hubble parameter, which yields a constant value of deceleration parameter. Physical and kinematical parameters of the models are discussed. The models are found to be compatibl…
We study a cosmological model composed of a dark energy fluid interacting with a viscous matter fluid in a spatially flat Universe. The matter component represents the baryon and dark matter and it is taken into account, through a bulk viscosity, the irreversible process that the matter fluid undergoes because of the accelerated expansion of the universe. The bulk viscous coefficient is assumed to be proportional to the Hubble parameter. The radiation component is also taken into account in the model. The model is constrained using the type Ia supernova observations, the shift parameter of the…
We consider the evolution of a flat, isotropic and homogeneous Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, that can be characterized by an ultra-relativistic equation of state and bulk viscosity coefficient obtained from recent lattice QCD calculations. The basic equation for the Hubble parameter is derived under the assumption that the total energy in the Universe is conserved. By assuming a power law dependence of bulk viscosity coefficient, temperature and relaxation time on energy density, an approximate solution of the field equations has bee…
Motivated by two seminal models proposed to explain the Universe acceleration, this paper is devoted to study a hybrid model which is constructed through a generalized Chaplygin gas with the addition of a bulk viscosity. We call the model a Viscous Generalized Chaplygin Gas (VGCG) and its free parameters are constrained through several cosmological data like the Observational Hubble Parameter, Type Ia Supernovae, Baryon Acoustic Oscillations, Strong Lensing Systems, HII Galaxies and using Joint Bayesian analysis. In addition, we implement a Om-diagnostic to analyze the VGCC dynamics and its di…
Bianchi type V viscous fluid cosmological model for barotropic fluid distribution with varying cosmological term $Λ$ is investigated. We have examined a cosmological scenario proposing a variation law for Hubble parameter $H$ in the background of homogeneous, anisotropic Bianchi type V space-time. The model isotropizes asymptotically and the presence of shear viscosity accelerates the isotropization. The model describes a unified expansion history of the universe indicating initial decelerating expansion and late time accelerating phase. Cosmological consequences of the model are also discusse…
The present study deals with spatially homogeneous and totally anisotropic Bianchi type V cosmological model in presence of bulk viscous fluid source with time dependent gravitational constant G and cosmological term Lambda. The coefficient of bulk viscosity zeta is considered to be a quadratic function of Hubble parameter H (i.e. zeta=zeta_0+zeta_1H+zeta_2H^2, where zeta_0, zeta_1 and zeta_2 are constants). Exact solution of Einstein's field equations are obtained by using a particular form of Hubble parameter H i.e. H(a)=m(a^-n +1), where m>0, n>1, a being a scale factor and H=(da/dt)/a whic…
Bulk viscosity is the only viscous influence that can change the background dynamics in a homogeneous and isotropic universe. In the present work, we analyze the bulk viscous cosmological model with the bulk viscosity coefficient of the form $ξ=ξ_0+ξ_1H+ξ_2\left(\frac{\dot{H}}{H}+H\right)$ where, $ξ_0$, $ξ_1$ and $ξ_2$ are bulk viscous parameters, and $H$ is the Hubble parameter. We investigate the impact of the bulk viscous parameter on dynamics of the universe in the recently proposed Weyl type $f(Q, T)$ gravity, where $Q$ is the non-metricity, and $T$ is the trace of the matter energy-momen…
In this paper, we first obtain the energy density by the approach of the new agegraphic dark energy model, and then the $f(T,B)$ gravity model is studied as an alternative to the dark energy in a viscous fluid by flat-FRW background, in which $T$ and $B$ are torsion scalar and boundary term. The Friedmann equations will obtain in the framework of modified teleparallel gravity by tetrad components. We consider that the universe dominates with components such as matter and dark energy by an interacting model. The Hubble parameter is parameterized by the power-law for the scale factor, and then w…
Reconstruction of f(G) Gravity from an Interacting Viscous Generalized QCD Ghost Dark Energy Model: Cosmology and Thermodynamics: Cosmology and Thermodynamics
Mukhtar Auezov South Kazakhstan University（穆赫塔尔·阿尤佐夫南哈萨克斯坦大学）；Amity University Kolkata（阿米提大学加尔各答分校）；L.N. Gumilyov Eurasian National University（L.N. 古米廖夫欧亚国立大学）
The objective of the present work is to study a cosmological model for a spatially flat Universe whose constituents are a dark energy field and a matter field which includes baryons and dark matter. The constituents are supposed to be in interaction and irreversible processes are taken into account through the inclusion of a non-equilibrium pressure. The non-equilibrium pressure is considered to be proportional to the Hubble parameter within the framework of a first order thermodynamic theory. The dark energy and matter fields are coupled by their barotropic indexes, which are considered as fu…
The Veneziano ghost field has been proposed as an alternative source of dark energy whose energy density is consistent with the cosmological observations. In this model, the energy density of QCD ghost field is expressed in terms of QCD degrees of freedom at zero temperature. We extend this model to finite temperature to search the model predictions from late time to early universe. We depict the variations of QCD parameters entering the calculations, dark energy density, equation of state, Hubble and deceleration parameters on temperature from zero to a critical temperature. We compare our re…
We study the static and spherically symmetric wormhole spacetime configurations at present time in a viscous universe. Considering three classes of viscous models, i.e., bulk viscosity as a function of Hubble constant $H_0$, present cosmic temperature $T_0$ and dark energy density $ρ_0$, respectively, we obtain several wormhole solutions. Through the analysis for the anisotropic solutions, we conclude that, to some extent, these three classes of viscous models have very high degeneracy with each other, and deviate slightly from the ideal fluid consequence. Subsequently, without the loss of gen…
We study the late acceleration of the universe by incorporating bulk viscous matter with the running vacuum. The vacuum energy density varies as the squares of the Hubble parameter ($ρ_Λ\propto H^2$), and the coefficient of bulk viscosity of matter is proportional to the velocity of expansion ($ξ\propto H$). We obtained an analytical solution to the Friedmann equations and estimated the model parameters using the combined data set SN1a+CMB+BAO+OHD. We have evaluated the universe's age as 14 Gyr, which is slightly higher than the age-predicted by the $Λ$CDM model. However, it is an improved res…
We assume cold dark matter to possess a small bulk-viscous pressure which typically attenuates the growth of inhomogeneities. Explicit calculations, based on Eckart's theory of dissipative processes, reveal that for viscous cold dark matter the usual Newtonian approximation for perturbation scales smaller than the Hubble scale is no longer valid. We advocate the use of a neo-Newtonian approach which consistently incorporates pressure effects into the fluid dynamics and correctly reproduces the general relativistic dynamics. This result is of interest for numerical simulations of nonlinear stru…
Constraining Cosmological Parameters with Viscous Modified Chaplygin Gas and Generalized Cosmic Chaplygin Gas Models in Horava-Lifshitz Gravity: Utilizing Late-time Datasets
We investigate cosmological models with two interacting fluids: dark energy and dark matter in flat Friedmann-Robertson-Walker universe. The interaction between dark energy and dark matter is described in terms of the parameters present in the inhomogeneous equation of state when allowance is made for bulk viscosity, for the Little Rip, the Pseudo Rip, and the bounce universes. We obtain analytic representation for characteristic properties in these cosmological models, in particular the bulk viscosity $ζ=ζ(H,t)$ as function of Hubble parameter and time. We discuss the corrections of thermodyn…
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 (excluding 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 i…
Based on the assumption that the dark energy possessing bulk viscosity is homogenously and isotropically permeated in the universe, we propose three new viscous dark energy (VDE) models to characterize the accelerating universe. By constraining these three models with the latest cosmological observations, we find that they just deviate very slightly from the standard cosmological model and can alleviate effectively the current $H_0$ tension between the local observation by the Hubble Space Telescope and the global measurement by the Planck Satellite. Interestingly, we conclude that a spatially…
We consider the inflation produced by two coupled fluids in the flat Friedmann-Robertson-Walker universe. Different cosmological models for describing inflation by use of an inhomogeneous equation of state for the fluid are investigated. The gravitational equations for energy and matter are solved, and analytic representations for the Hubble parameter and the energy density are obtained. Corrections in the energy density for matter inducing the inflation and the coupling with energy are discussed. We analyze the description of inflation induced by non-constant equation-of-state parameters from…
We study the phantom fluid in the late universe, thus assuming the equation of state parameter $w$ to be less than $-1$. The fluid is assumed to consist of two components, one laminar component $ρ$ and one turbulent component $ρ_T$, the latter set proportional to $ρ$ as well as to the Hubble parameter, $ρ_T =3τHρ$ with $τ$ a positive constant associated with the turbulence. The effective energy density is taken to be $ρ_e= ρ+ ρ_T$, and the corresponding effective pressure is $p_e=w ρ_e$, with $w$ constant. These basic assumptions lead to a Big Rip universe; the physical quantities diverging du…
Recent studies indicate that, near equilibrium condition could not be maintained for bulk viscous matter models during the accelerated expansion of the universe in the context of Einstein's gravity, without including the cosmological constant. But from our investigation in $f(R,T)$ gravity, it is observed that, this condition can be satisfied in this modified gravity regime by properly constraining the coupling and viscous parameters. Accordingly, strict constraints are developed for free parameters in bulk viscous models in $f(R,T)=R+2λT$ gravity based on fulfillment near equilibrium conditio…
In this paper, we study the model of $f(T, B)$ gravity with viscous fluid in flat-FRW metric, in which $T$ and $B$ are torsion scalar and boundary term, respectively. We obtain the Friedmann equations in the framework of modified teleparallel gravity by tetrad components. We consider an interacting model between matter and dark energy so that universe dominates by viscous fluid. Then, we write the corresponding cosmological parameters in terms of the redshift parameter, and, we parameterize the Hubble parameter with experimental data. In what follows, we plot the corresponding cosmological par…
We use the hybrid model of bulk viscosity and generalized chaplygin gas (GCG), named the viscous generalized chaplygin gas (VGCG) model, which is thought to be an alternate dark fluid of the universe. We explore the dynamics of the VGCG model in the framework of the non-metricity $f(Q)$ gravity using the functional form $f(Q)=βQ^n$, where $β$ and $n$ are arbitrary constants. For the purpose of constraining model parameters, we use recent observational datasets such as Observational Hubble data, Baryon Acoustic Oscillations, and Type $Ia$ supernovae data. According to our study, the evolution o…
Inspired by thermodynamical dissipative phenomena, we consider bulk viscosity for dark fluid in a spatially flat two-component Universe. Our viscous dark energy model represents Phantom crossing avoiding Big-Rip singularity. We propose a non-minimal derivative coupling scalar field with zero potential leading to accelerated expansion of Universe in the framework of bulk viscous dark energy model. In this approach, coupling constant ($κ$) is related to viscosity coefficient ($γ$) and energy density of dark energy at the present time ($Ω_{\rm DE}^0$). This coupling is bounded as $κ\in [-1/9H_0^2…
Bulk viscous cosmological models with a cosmological constant: Observational constraints
Universidad de La Serena（拉塞雷纳大学）；Universidad de Santiago de Chile（圣地亚哥智利大学）；Center for Interdisciplinary Research in Astrophysics and Space Exploration (CIRAS)（天体物理学与空间探索跨学科研究中心）；Instituto de Astrofísica de Canarias（加那利群岛天体物理研究所）；Universidad de La Laguna（拉古纳大学）
We propose a new model for the viscosity of cosmic matters, which can be applied to different epochs of the universe. Using this model, we include the bulk viscosities as practical corrections to the perfect fluid models of the baryonic and dark matters since the material fluids in the real world may have viscosities due to thermodynamics. Such inclusion is put to the test within the framework of $f(T)$ gravity that is proved to be successful in describing the cosmic acceleration, where $T$ denotes the torsion scalar. We perform an observational fit to our model and constrain the cosmological …
In this paper, we have presented bulk viscous cosmological model of the universe in the modified gravity theory in which the Lagragian of the gravitational action contains a general function $f(R, T) $, where $R$ and $T$ denote the curvature scalar and the trace of the energy-momentum tensor respectively, in the framework of a flat Friedmann-Robertson-Walker model with isotropic fluid. We obtain cosmological solution in $f(R,T)$ theory of gravity, specially of particular choice $f(R,T)=R+2λT$, where $λ$ is a constant, in the presence of bulk viscosity that are permitted in Eckart theory, Trunc…
Based on hot big bang theory, the cosmological matter is conjectured to undergo QCD phase transition(s) to hadrons, when the universe was about $1-10 μ$s old. In the present work, we study the quark-hadron phase transition, by taking into account the effect of the bulk viscosity. We analyze the evolution of the quantities relevant for the physical description of the early universe, namely, the energy density $ρ$, temperature $T$, Hubble parameter $H$ and scale factor $a$ before, during and after the phase transition. To study the cosmological dynamics and the time evolution we use both analyti…
Evolution of the bulk viscous matter dominated universe has been analysed using the full causal, Israel-Stewart theory for the evolution of bulk viscous pressure in the context of recent acceleration of the universe. The form of bulk viscosity is taken as $ξ=αρ^{1/2}. $ We obtained analytical solutions for the Hubble parameter and scale factor of the universe. The model parameters have been computed using the Type Ia supernovae observational data. The evolution of the prominent cosmological parameters were obtained. The age of the universe for the best estimated model parameters is found to be…
Some cosmological scenarios with bulk viscosity for the dark energy fluid are considered. Based on some considerations related to hydrodynamics, two different equations of state for dark energy are assumed, leading to power-law and logarithmic effective corrections to the pressure. The models are tested with the latest astronomical data from Type Ia supernovae (Pantheon sample), measurements of the Hubble parameter $H(z)$, Baryon Acoustic Oscillations and Cosmic Microwave Background radiation. In comparison with $Λ$CDM model, some different results are obtained and their viability is discussed…
In this paper, we have investigated a bulk viscous anisotropic Universe and constrained its model parameters with recent $H(z)$ and Pantheon compilation data. Using cosmic chronometric technique, we estimate the present value of Hubble's constant as $H_{0} = 69.39 \pm 1.54~km~s^{-1}Mpc^{-1}$, $70.016 \pm 1.65~km~s^{-1}Mpc^{-1}$ and $69.36 \pm 1.42~km~s^{-1}Mpc^{-1}$ by bounding our derived model with recent $H(z)$ data, Pantheon and joint $H(z)$ and Pantheon data respectively. The present age of the Universe is specified as $t_0= 0.9796H_0^{-1}\sim 13.79$ Gyrs. The model favours a transitionin…
In this talk, we discuss one of the dissipative processes which likely take place in the Early Universe. We assume that the matter filling the isotropic and homogeneous background is to be described by a relativistic viscous fluid characterized by an ultra-relativistic equation of state and finite bulk viscosity deduced from recent lattice QCD calculations and heavy-ion collisions experiments. We concentrate our treatment to bulk viscosity as one of the essential dissipative processes in the rapidly expanding Early Universe and deduce the dependence of the scale factor and Hubble parameter on …
We study a phenomenological dark energy model which is rooted in the Veneziano ghost of QCD. In this dark energy model, the energy density of dark energy is proportional to Hubble parameter and the proportional coefficient is of the order $Λ^3_{QCD}$, where $Λ_{QCD}$ is the mass scale of QCD. The universe has a de Sitter phase at late time and begins to accelerate at redshift around $z_{acc}\sim0.6$. We also fit this model and give the constraints on model parameters, with current observational data including SnIa, BAO, CMB, BBN and Hubble parameter data. We find that the squared sound speed o…
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 universe, and analytic expressions …
In this paper, a spatially homogeneous and anisotropic Bianchi type V model filled with an imperfect fluid with bulk viscosity and particle creation, is investigated within the framework of General Relativity. Particle creation and bulk viscosity have been considered as separate irreversible processes. The energy- momentum tensor is modified to accommodate the viscous pressure and creation pressure which is associated with creation of matter out of gravitational field. Exact solutions of the field equations are obtained by applying a special law of variation of Hubble parameter. Using this ass…
