scholarly journals Stability Analysis of Bulk Viscous Cosmology

2018 ◽  
Vol 168 ◽  
pp. 08006 ◽  
Author(s):  
M. Sharif ◽  
Saadia Mumtaz
Keyword(s):  
Power Law ◽  
Bulk Viscosity ◽  
Viscosity Coefficient ◽  
Study Phase ◽  
Universe Model ◽  
Power Law Model ◽  
Frw Universe ◽  
Dimensionless Variables ◽  
The Stability ◽  
Bulk Viscosity Coefficient

In this paper, we study phase space analysis of FRW universe model by taking a power-law model for bulk viscosity coefficient. An autonomous system of equations is developed by defining normalized dimensionless variables. We find corresponding critical points for di.erent values of the parameters to investigate stability of the system. It is found that the presence of power-law model of bulk viscosity appears as an e.ective ingredient to enhance the stability of the respective universe model.

Vorticity generated by sound

1954 ◽  
Vol 226 (1164) ◽  
pp. 7-16 ◽  
Keyword(s):  
Wind Speed ◽  
Bulk Viscosity ◽  
Viscosity Coefficient ◽  
Order Effects ◽  
Relaxation Processes ◽  
Acoustic Disturbances ◽  
Specific Heats ◽  
Coefficient Of Viscosity ◽  
Bulk Viscosity Coefficient ◽  
Intermolecular Relaxation

A revision is given of the basic theory of second-order effects caused by acoustic disturbances in a fluid, especially the vorticity giving rise to the ultrasonic wind, which was first explained by Eckart. The ultrasonic wind is produced by the interaction of the radiative and the non-radiative components of the acoustic motion. The wind speed is for the most part proportional to the acoustic attenuation coefficient. Wind-speed measurements thus usually furnish no more information about the second coefficient of viscosity, or the bulk viscosity, than do other attenuation measurements. It appears reasonable to regard the Stokesian bulk viscosity coefficient as a parameter of intramolecular and intermolecular relaxation processes. It does not have a unique value for all frequencies. Provided other parameters such as the coefficients of shear viscosity and heat conduction, and the specific heats are known independently, this effective bulk viscosity can be evaluated from any type of attenuation measurement. Measurements over large enough frequency ranges can distinguish among the contributions of different relaxation processes to the effective bulk viscosity coefficient.

scholarly journals STUDY OF THE QUASI-ISOTROPIC SOLUTION NEAR THE COSMOLOGICAL SINGULARITY IN THE PRESENCE OF BULK VISCOSITY

2008 ◽  
Vol 17 (06) ◽  
pp. 881-896 ◽  
Author(s):  
NAKIA CARLEVARO ◽  
GIOVANNI MONTANI
Keyword(s):  
Power Law ◽  
Bulk Viscosity ◽  
Dynamical Behavior ◽  
Viscosity Coefficient ◽  
Viscous Effects ◽  
Isotropic Universe ◽  
Cosmological Singularity ◽  
Isotropic Solution ◽  
Second Order In Time ◽  
The Universe

We analyze the dynamical behavior of a quasi-isotropic universe in the presence of a cosmological fluid endowed with bulk viscosity. We express the viscosity coefficient as a power law of the fluid energy density: ζ = ζ0∊s. Then we fix s = 1/2 as the only case in which viscosity plays a significant role in the singularity physics but does not dominate the universe dynamics (as required by its microscopic perturbative origin). The parameter ζ0is left free to define the intensity of the viscous effects.In spirit of the work by Lifshitz and Khalatnikov on the quasi-isotropic solution, we analyze both Einstein and hydrodynamic equations up to first and second order in time. As a result, we get a power law solution existing only in correspondence to a restricted domain of ζ0.

scholarly journals Viscous cosmology in the Weyl-type f(Q, T) gravity

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Gaurav N. Gadbail ◽  
Simran Arora ◽  
P. K. Sahoo
Keyword(s):  
Bulk Viscosity ◽  
Viscosity Coefficient ◽  
Momentum Tensor ◽  
Model Parameters ◽  
Field Equations ◽  
Eos Parameter ◽  
Bulk Viscous ◽  
The Impact ◽  
Bulk Viscosity Coefficient ◽  
The Universe

AbstractBulk 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 $$\zeta =\zeta _0+\zeta _1H+\zeta _2\left( \frac{\dot{H}}{H}+H\right) $$ ζ = ζ 0 + ζ 1 H + ζ 2 H ˙ H + H where, $$\zeta _0$$ ζ 0 , $$\zeta _1$$ ζ 1 and $$\zeta _2$$ ζ 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–momentum tensor. The exact solutions to the corresponding field equations are obtained with the viscous fluid and the linear model of the form $$f(Q, T)=\alpha Q+\frac{\beta }{6\kappa ^2}T$$ f ( Q , T ) = α Q + β 6 κ 2 T , where $$\alpha $$ α and $$\beta $$ β are model parameters. Further, we constrain the model parameters using the 57 points Hubble dataset the recently released 1048 points Pantheon sample and the combination Hz + BAO + Pantheon, which shows our model is good congeniality with observations. We study the possible scenarios and the evolution of the universe through the deceleration parameter, the equation of state (EoS) parameter, the statefinder diagnostics, and the Om diagnostics. It is observed that the universe exhibits a transition from a decelerated to an accelerated phase of the universe under certain constraints of model parameters.

HIGHER DIMENSIONAL COSMOLOGICAL MODEL IN LYRA GEOMETRY: REVISITED

2003 ◽  
Vol 12 (05) ◽  
pp. 853-860 ◽  
Author(s):  
G. P. SINGH ◽  
S. KOTAMBKAR ◽  
ANIRUDH PRADHAN
Keyword(s):  
Cosmological Model ◽  
Power Law ◽  
Bulk Viscosity ◽  
Research Work ◽  
Lyra Geometry ◽  
Universe Model ◽  
Higher Dimensional ◽  
Empty Universe ◽  
Kaluza Klein

In this paper we have revisited the research work of Rahman and Bera22on Kaluza–Klein cosmological model within the framework of Lyra Geometry. It has been shown that the empty universe model yields a power law relation without any assumption. The role of bulk viscosity on five-dimensional cosmological model is discussed. The physical behaviour of the models is examined in all cases.

DECELERATING CAUSAL BULK VISCOUS COSMOLOGICAL MODELS

2000 ◽  
Vol 09 (02) ◽  
pp. 97-110 ◽  
Author(s):  
T. HARKO ◽  
M. K. MAK
Keyword(s):  
Relaxation Time ◽  
Bulk Viscosity ◽  
Viscosity Coefficient ◽  
State Equation ◽  
Cosmological Models ◽  
Boltzmann Gas ◽  
Bulk Viscous ◽  
Barotropic Equation ◽  
Bulk Viscosity Coefficient ◽  
The Universe

The dynamics of a causal bulk viscous cosmological fluid filled flat constantly decelerating noninflationary Robertson–Walker spacetime is considered. The matter component of the Universe is assumed to satisfy a linear barotropic equation of state and the state equation of the small temperature Boltzmann gas. The resulting cosmological models satisfy the condition of smallness of the viscous stress. The evolution of the relaxation time, temperature, bulk viscosity coefficient and comoving entropy of the dissipative cosmological fluid are obtained by assuming several bulk viscosity coefficient-relaxation time relations.

scholarly journals ON THE ROLE OF VISCOSITY IN EARLY COSMOLOGY

2008 ◽  
Vol 23 (08) ◽  
pp. 1248-1252
Author(s):  
NAKIA CARLEVARO ◽  
GIOVANNI MONTANI
Keyword(s):  
Energy Density ◽  
Power Law ◽  
Bulk Viscosity ◽  
Viscosity Coefficient ◽  
Hydrodynamic Equations ◽  
Restricted Domain ◽  
Asymptotic Approach ◽  
Cosmological Singularity ◽  
Second Order In Time

We present a discussion of the effects induced by bulk viscosity on the very early Universe stability. The viscosity coefficient is assumed to be related to the energy density ρ via a power-law of the form ζ = ζ0ρs (where ζ0, s = const.) and the behavior of the density contrast in analyzed. In particular, we study both Einstein and hydrodynamic equations up to first and second order in time in the so-called quasi-isotropic collapsing picture near the cosmological singularity. As a result, we get a power-law solution existing only in correspondence to a restricted domain of ζ0. The particular case of pure isotropic FRW dynamics is then analyzed and we show how the asymptotic approach to the initial singularity admits an unstable collapsing picture.

scholarly journals Continuum perspective of bulk viscosity in compressible fluids

2017 ◽  
Vol 812 ◽  
pp. 966-990 ◽  
Author(s):  
Xin-Dong Li ◽  
Zong-Min Hu ◽  
Zong-Lin Jiang
Keyword(s):  
Relaxation Time ◽  
Bulk Viscosity ◽  
Viscosity Coefficient ◽  
Linear Increase ◽  
Compressible Fluids ◽  
Theoretical Formula ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Bulk Viscosity Coefficient ◽  
The Continuum

Kinetic theory and acoustic measurements have proven that the bulk viscosity associated with the expansion or compression effect cannot be ignored in compressible fluids except for monatomic gases. A new theoretical formula for the bulk viscosity coefficient (BVC) $\unicode[STIX]{x1D701}$ is derived by the continuum medium methodology, which provides a further understanding of the bulk viscosity, i.e. $\unicode[STIX]{x1D701}$ is equal to the product of the bulk modulus $K$ and the relaxation time $\unicode[STIX]{x1D70F}$ ($\unicode[STIX]{x1D701}=K\unicode[STIX]{x1D70F}$). The continuum and kinetic theories present consistent results from macro- and microperspectives respectively, only differing in terms of a coefficient. The theoretical predictions of the BVC in diatomic molecules, such as $\text{N}_{2}$, $\text{O}_{2}$ and CO, show good agreement with the experimental data over a wide range of temperature. In addition, the vibrational contributions to $\unicode[STIX]{x1D701}$ are controlled by a rapid exponential decrease at high temperatures, while at low temperatures a slow linear increase proceeds for the rotational cases. The relaxation time $\unicode[STIX]{x1D70F}$, collision number $Z$, BVC $\unicode[STIX]{x1D701}$ and ratio of bulk-to-shear viscosities $\unicode[STIX]{x1D701}/\unicode[STIX]{x1D707}$ in the vibrational mode are found to be several orders of magnitude larger than those in the rotational mode.

scholarly journals Thermodynamics in the viscous early universe

2010 ◽  
Vol 88 (11) ◽  
pp. 825-831 ◽  
Author(s):  
A. Tawfik
Keyword(s):  
Early Universe ◽  
Bulk Viscosity ◽  
Viscosity Coefficient ◽  
Matter Content ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Curvature Parameter ◽  
Radical Revision ◽  
Bulk Viscosity Coefficient ◽  
The Universe

Assuming that the matter in the background geometry is a free gas and that no phase transitions were occurring in the early Universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, the scaling factor a, and the curvature parameter k, can be derived from this simple model, which on one hand fulfills and entirely obeys the laws of thermodynamics, and on the other hand, its results are compatible with the Friedmann–Robertson–Walker model and the Einstein field equations. Including a finite bulk viscosity coefficient leads to important changes in all these cosmological quantities. Accordingly, our picture about the evolution of the Universe and its astrophysical consequences seems to undergoing a radical revision. We find that k strongly depends on the thermodynamics of background matter. The time scale at which negative curvature might take place depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we introduce expressions for H and the bulk viscosity coefficient ξ.

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