Narrow Results

We investigate the existence and properties of traveling wave solutions for the hyperbolic-elliptic system of conservation laws describing the dynamics of van der Waals fluids. The model is based on a constitutive equation of state containing two inflection points and incorporates nonlinear viscosity and capillarity terms. A global description of the traveling wave solutions is provided. We distinguish between classical and non-classical trajectories and, for the latter, the existence and properties of kinetic functions is investigated. An earlier work in this direction (cf. [4]) was restricted to dealing with one inflection point only. Specifically, given any left-hand state and any shock speed (within some admissible range), we prove the existence of a non-classical traveling wave for a sequence of parameter values representing the ratio of viscosity and capillarity. Our analysis exhibits a surprising lack of monotonicity of traveling waves. The behavior of these non-classical trajectories is also investigated numerically.

The inflationary expansion of our early-time universe is considered in terms of the van der Waals equation, as equation of state for the cosmic fluid, where a bulk viscosity contribution is assumed to be present. The corresponding gravitational equations for the energy density in a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker universe are solved, and an analytic expression for the scale factor is obtained. Attention is paid, specifically, to the role of the viscosity term in the accelerated expansion; the values of the slow-roll parameters, the spectral index, and the tensor-to-scalar ratio for the van der Waals model are calculated and compared with the most recent astronomical data from the Planck satellite. By imposing reasonable restrictions on the parameters of the van der Waals equation, in the presence of viscosity, it is shown to be possible for this model to comply quite precisely with the observational data. One can therefore conclude that the inclusion of viscosity in the theory of the inflationary epoch may definitely improve the cosmological models.

We present perfect fluid Bianchi type-I cosmological models with time-dependent cosmological term $\mathrm{\Lambda }$. Exact solutions of the Einstein’s field equations are presented via a suitable functional form for Hubble parameter $H$, which yields a model of the universe that represents initially decelerating and late-time accelerating expansion. We discuss, in the context of some vacuum decay laws, cosmological implications of the corresponding solutions. The physical and geometrical features of the models are also discussed.

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 $f(R,T)=R+2\lambda T$, where $\lambda$ is a constant, in the presence of bulk viscosity that are permitted in Eckart theory, Truncated Israel Stewart (TIS) theory and Full Israel Stewart (FIS) theory. The physical and geometrical properties of the models in Eckart, TIS theory and FIS theory are studied in detail. The analysis of the variation of bulk viscous pressure, energy density, scale factor, Hubble parameter and deceleration parameter with cosmic evolution is done in the respective theories. The models are analyzed by comparison with recent observational data. The cosmological models are compatible with observations.

Cosmological models with an inhomogeneous viscous dark fluid, coupled with dark matter in the Friedmann–Robertson–Walker (FRW) flat universe, are considered. The influence of thermal effects caused by Hawking radiation on the visible horizon is studied, in connection with the classified Types I and III singularities which are known to occur within a finite amount of time. Allowance of thermal effects implies that a transition to a Type II singularity can take place, in a finite time. We take into account a bulk viscosity of the dark fluid, observing the equation of state in the case of radiation, and find that there is a qualitative change in the singular universe of Type I: it may pass into a singularity of Type III, or it may avoid the singularity at all.

In this paper, we study two different cases of inhomogeneous EOS of the form $p_d=w(t){\rho }_d+w_{1}f(H,t)$. We derive the energy density of dark fluid and dark matter component for both the cases. Further, we calculate the evolution of energy density, gravitational constant and cosmological constant. We also explore the finite time singularity and thermodynamic stability conditions for the two cases of EOS. Finally, we discuss the thermodynamics of inhomogeneous EOS with the derivation of internal energy, Temperature and entropy and also show that all the stability conditions are satisfied for the two cases of EOS.

In this paper, we investigate the thermodynamics of a dark energy bulk viscosity model as a cosmic fluid. In this regard, the two theories of Eckart and Israel–Stewart (IS) are the bases of our work. Therefore, we first investigate the thermodynamics of cosmic fluids in the dark energy bulk viscosity model and the general relationships. Then, we express the thermodynamic relationships of Eckart’s theory. Due to the basic equations of Eckart’s theory and Friedmann’s equations, we consider two states, one is $p=-\rho$ (standard) and the other is $p\ne -\rho$ (non-standard). In the standard state, we define the pressure $(p)$, energy density $(\rho )$ and bulk viscosity coefficient $(\xi )$ of the cosmic fluid in terms of cosmic time and we obtain its relations. We also mention that in this standard state, because of $p=-\rho$, the value of $a(t)$ is zero, so $a(t)$ is not defined in this state. But in the non-standard case $(p\ne -\rho )$, the bulk viscosity coefficient $(\xi )$ is zero and only the scale factor, pressure and energy density of the cosmic fluid are defined. We also consider two states of constant and variable bulk viscosity coefficients and obtain three Hubble constant parameters and scale factor in terms of cosmic time, and energy density in terms of scale factor. In the state of variable bulk viscosity coefficient, we consider the viscosity coefficient as the power law from energy density $(\xi =\alpha {\rho }^s)$, which is $\alpha >0$ and a constant. Following this, we discuss about the dissipative effects of cosmic fluids and examine the effects of energy density for dark energy in the IS theory. The results are comprehensively presented in Tables 1 and 2. Also, according to observational constraints, the results of the likelihood analysis for the IS viscous model are summarized in Table 3.

In this paper, we have presented bulk viscous cosmological model of the universe in the modified gravity in which the Lagrangian of the gravitational action contains a general function $F(T)$, where $T$ denotes torsion, for flat Friedmann–Robertson–Walker spacetime with isotropic fluid. We have studied cosmological solution in $F(T)$ theory of gravity, especially of a particular preference $F(T)=T+f(T)=(1+\gamma )T+\alpha T^2$, where $\gamma$ and $\alpha$ are coupling constants, in the presence of bulk viscosity described by Eckart theory, Truncated Israel Stewart theory and Full Israel Stewart theory. The physical and geometrical prospectives of the models in Eckart, Truncated Israel Stewart theory and Full Israel Stewart theory are deliberated in details. The investigation of the variation of bulk viscous pressure, energy density, scale factor, Hubble parameter and deceleration parameter with cosmic growth is furnished in the relevant theories. The models are analyzed by comparison with recent observational data. The cosmological models are well-matched with observations.

We construct a new family of entropy stable difference schemes which retain the precise entropy decay of the Navier–Stokes equations,