scholarly journals Viscous Matter in FRW Cosmology

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1269
Author(s):  
Marek Szydłowski ◽  
Adam Krawiec
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Viscosity Coefficient ◽  
Chaplygin Gas ◽  
Dynamical Problem ◽  
Frw Cosmology ◽  
Singularity Problem ◽  
Viscosity Effects ◽  
Simple Theorem ◽  
Standard Cosmological Model

We investigate the dynamics of dust matter with bulk viscosity effects. We explored the analogy dynamical problem to Chaplygin gas. Due to this analogy we give exact solutions for the FRW cosmology with viscosity coefficient parameterized by the Belinskii–Khalatnikov power law dependence with respect to energy density. These exact solutions are given in the form of hypergeometrical functions. We proved simple theorem which illustrated as viscosity effects can solved the initial singularity problem present in standard cosmological model.

scholarly journals Dynamical system analysis of FLRW models with Modified Chaplygin gas

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ali Osman Yılmaz ◽  
Ertan Güdekli
Keyword(s):  
Dynamical System ◽  
Equation Of State ◽  
Energy Density ◽  
System Analysis ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
State Spaces ◽  
The Universe ◽  
Matter Energy ◽  
Far Future

AbstractWe investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. We assume $$p=(\gamma -1)\mu -\dfrac{A}{\mu ^\alpha }$$ p = ( γ - 1 ) μ - A μ α as equation of state where $$\mu$$ μ is the matter-energy density, p is the pressure, $$\alpha$$ α is a parameter which can take on values $$0<\alpha \le 1$$ 0 < α ≤ 1 as well as A and $$\gamma$$ γ are positive constants. We draw the state spaces and analyze the nature of the singularity at the beginning, as well as the fate of the universe in the far future. In particular, we address the question whether there is a solution which is stable for all the cases.

FRW viscous modified cosmic Chaplygin gas cosmology in the presence of cosmological constant

2019 ◽  
Vol 16 (09) ◽  
pp. 1950141 ◽  
Author(s):  
G. S. Khadekar ◽  
Aina Gupta ◽  
Kalpana Pande
Keyword(s):  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Chaplygin Gas ◽  
Frw Universe ◽  
Dark Energy Density ◽  
Linear Combinations ◽  
Linear Differential ◽  
The Stability ◽  
Cardassian Universe

In this paper, we study viscous Modified Cosmic Chaplygin Gas (MCCG) in the presence of cosmological constant in flat FRW universe. We assume that bulk viscosity [Formula: see text] and cosmological constant [Formula: see text] are the linear combinations of two terms, one is constant and other is a function of dark energy density [Formula: see text]. In this framework, we solve the non-linear differential equation analytically and numerically and obtain time dependent dark energy density. We also consider two separate cases of early and late universe and discussed the evolution of dark energy density. We investigate the effect of viscosity and cosmological constant to the evolution of universe and discuss the stability of the model by square of speed of sound. Finally, we compare our model with Cardassian universe.

scholarly journals Nonlinear Schrödinger-type formulation of scalar field cosmology: Two barotropic fluids and exact solutions

2020 ◽  
Vol 35 (19) ◽  
pp. 2050157
Author(s):  
Chonticha Kritpetch ◽  
Jarunee Sanongkhun ◽  
Pichet Vanichchapongjaroen ◽  
Burin Gumjudpai
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Time Dependent ◽  
Frw Cosmology ◽  
Dependent Case ◽  
Nonlinear Schrödinger ◽  
Barotropic Fluids ◽  
Scalar Field Cosmology ◽  
Formulation Variables ◽  
Canonical Scalar Field

Time-independent nonlinear Schrödinger-type (NLS) formulation of FRW cosmology with canonical scalar field is considered in the case of two barotropic fluids. We derived Friedmann formulation variables in terms of NLS variables. Seven exact solutions found by D’Ambroise [Ph.D. thesis, arXiv:1005.1410 ] and one new found solution are explored and tested in cosmology. The result suggests that time-independent NLS formulation of cosmology case should be upgraded to the time-dependent case.

DOMAIN WALLS IN HIGHER DIMENSIONS

1998 ◽  
Vol 07 (01) ◽  
pp. 81-88
Author(s):  
A. BANERJEE ◽  
AJANTA DAS
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Domain Walls ◽  
Stress Component ◽  
Higher Dimensions ◽  
Dimensional Spacetime ◽  
Thick Domain Walls

Thick domain walls with nonvanishing stress component in the direction perpendicular to the plain of the wall are considered. Their exact solutions are obtained in the background of a five-dimensional spacetime. There may be both expanding and collapsing walls. The energy density decreases on both sides of the walls and the spacetime in all cases is found to be reflection symmetric with respect to the walls.

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

scholarly journals DARK ENERGY IN GLOBAL BRANE UNIVERSE

2007 ◽  
Vol 16 (10) ◽  
pp. 1633-1640 ◽  
Author(s):  
YONGLI PING ◽  
LIXIN XU ◽  
CHENGWU ZHANG ◽  
HONGYA LIU
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Energy Density ◽  
Exact Solutions ◽  
Deceleration Parameter ◽  
Mass Density ◽  
Density Parameter ◽  
Dark Energy Density ◽  
Friedmann Equations

We discuss the exact solutions of brane universes and the results indicate that the Friedmann equations on the branes are modified with a new density term. Then, we assume the new term as the density of dark energy. Using Wetterich's parametrization equation of state (EOS) of dark energy, we obtain that the new term varies with the redshift z. Finally, the evolutions of the mass density parameter Ω2, dark energy density parameter Ωx and deceleration parameter q2 are studied.

scholarly journals VISCOUS MODIFIED COSMIC CHAPLYGIN GAS COSMOLOGY

2013 ◽  
Vol 22 (09) ◽  
pp. 1350061 ◽  
Author(s):  
B. POURHASSAN
Keyword(s):  
Dark Energy ◽  
Energy Density ◽  
Nonlinear Equation ◽  
Observational Data ◽  
Function Method ◽  
Chaplygin Gas ◽  
Time Dependent ◽  
Dark Energy Density ◽  
Hubble Expansion ◽  
Exponential Function Method

In this paper, we construct viscous modified cosmic Chaplygin gas as a model of dark energy. We use exponential function method to solve nonlinear equation and obtain time-dependent dark energy density. Then, we discuss Hubble expansion parameter and scale factor and fix them by using observational data. Effect of viscosity to the evolution of Universe is investigated. We also investigate stability of this theory.

scholarly journals Wormhole solutions in f(R) gravity theory for Chaplygin gas scenario

2021 ◽  
pp. 2150119
Author(s):  
Bikram Ghosh ◽  
Saugata Mitra
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Chaplygin Gas ◽  
Tidal Force ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Shape Functions ◽  
Tangential Pressure ◽  
Constant Energy ◽  
State Formula

This paper deals with some wormhole solutions which are obtained by taking two different shape functions along with zero tidal force. For obtaining wormhole solutions, anisotropic fluid and a equation of state [Formula: see text] related by Chaplygin gas are considered, where [Formula: see text] is the energy density, [Formula: see text] is tangential pressure and [Formula: see text] is positive constant. Energy conditions are examined for two different models, and it is found that major energy conditions are satisfied in a region.

Viscosity Effects on the Propagation of Acoustic Transients

2000 ◽  
Author(s):  
G. C. Gaunaurd ◽  
G. C. Everstine
Keyword(s):  
Analytic Solution ◽  
Propagation Speed ◽  
Viscosity Coefficient ◽  
Viscous Medium ◽  
Initial Value ◽  
One Dimensional ◽  
Impulsive Excitation ◽  
Viscosity Effects ◽  
Parabolic Pde ◽  
Acoustic Transients

Abstract The propagation of an impulsive excitation applied at the origin of a lossy viscous medium is studied by operational techniques as the excitation advances through the medium. The solution of the governing partial differential equation (PDE) for such transient propagation problems has been elusive. Such solution is found and quantitatively examined here using a one-dimensional model in space and time. As expected, as the transient advances through space, its amplitude decreases, and its width broadens. Such is the damping effect of viscosity that one would anticipate from elementary considerations in related disciplines such as electrodynamics. Such is also the smoothing-out effect of dispersion. We also obtain an approximate solution of the present boundary-initial value problem based on the method of steepest descents. This approximation agrees with the first term of the complete analytic solution given here. The pertinent dispersion relation associated with the governing parabolic PDE is shown to impose a restrictive condition on the allowable values of the propagation speed and the kinematic viscosity coefficient, thus assuring that propagation with attenuation does take place. Various numerical results illustrate and quantitatively describe the propagation of the transient pulse in several nondimensional graphs.

Modified Chaplygin gas equation of state on viscous dissipative extended holographic Ricci dark energy and the cosmological consequences

2016 ◽  
Vol 26 (06) ◽  
pp. 1750042 ◽  
Author(s):  
Surajit Chattopadhyay
Keyword(s):  
Dark Energy ◽  
Bulk Viscosity ◽  
Cold Dark Matter ◽  
Viscosity Coefficient ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
Ricci Dark Energy ◽  
Dissipative Term ◽  
Generalized Second Law ◽  
The Universe

The present paper reports a study on modified Chaplygin gas (MCG)-based reconstruction scheme for extended holographic Ricci dark energy (EHRDE) in the presence of viscous type dissipative term. The dissipative effect has been described by using Eckart approach. Under the assumption that the universe is filled with MCG–EHRDE under the influence of bulk viscosity we have studied the cosmological dynamics, where the bulk viscosity coefficient has been chosen in a particular time varying form [Formula: see text], where [Formula: see text] and [Formula: see text] are constant coefficients and [Formula: see text] is the Hubble parameter. Furthermore, we have reconstructed the potential and dynamics of viscous MCG–EHRDE as scalar field. Thereafter we have studied the statefinder trajectories to discern its departure from [Formula: see text] cold dark matter ([Formula: see text]CDM) and finally investigated validity of the generalized second law (GSL) of thermodynamics considering event horizon as the enveloping horizon of the universe.

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