Non-perfect Fluid Research Articles

The matter Lagrangian of a non-perfect fluid

We show that the matter Lagrangian of a non-perfect fluid takes the negative or positive value of the total energy density of the fluid, which is composed of the rest plus internal energy densities. The ambiguity of the sign depends on the definition of the matter action and the chosen signature.

Metric-affine gravity: Nonmetricity of space as dark matter/energy ?

A possibility of using a metric-affine theory to consider dark matter and dark energy through the properties of nonmetricity is discussed. In the framework of proposed metric-affine theory, the gravity field is described by the standard Einstein tensor, which depends only on the metric tensor and its derivatives. The nonmetricity and torsion are considered as property of space–time, which is source gravity that can be interpreted as a specific (maybe dark) form of matter and energy. This form of matter and energy, which are described by nonmetricity and torsion tensors, are sources of ”metric” gravity. For the observers, these non-metric properties are manifested as the specific properties of perfect (or non-perfect) fluid interacting with metric gravity only. The proposed metric-affine theory cannot be considered as standard theory of metric-affine gravity. The suggested theory is the metric theory of gravity and the affine theory of a specific (dark) form of matter and energy. The stress–energy tensor of this specific matter and energy is described by the non-metric part of the generalized (metric-affine) Einstein tensor. The specific matter and energy manifest itself as specific perfect or non-perfect fluid (and its energy), which interacts with standard matter only through gravity. The non-metric part is described as a stress–energy tensor, which is supposed to be considered as a candidate for the role of a stress–energy tensor of dark matter/energy. The article discusses a potential possibility to assume that nonmetricity simulates dark matter/energy by introducing a new source term of gravity into general relativity.

Study of a Viscous ΛWDM Model: Near-Equilibrium Condition, Entropy Production, and Cosmological Constraints

Extensions to a ΛDM model have been explored in order to face current tensions that occur within its framework, which encompasses broadening the nature of the dark matter (DM) component to include warmness and a non-perfect fluid description. In this paper, we investigated the late-time cosmological evolution of an exact solution recently found in the literature, which describes a viscous warm ΛDM model (ΛWDM) with a DM component that obeys a polytropic equation of state (EoS), which experiences dissipative effects with a bulk viscosity proportional to its energy density, with proportionality constant ξ0. This solution has the particularity of having a very similar behavior to the ΛCDM model for small values of ξ0, evolving also to a de Sitter type expansion in the very far future. We explore firstly the thermodynamic consistences of this solution in the framework of Eckart’s theory of non-perfect fluids, focusing on the fulfillment of the two following conditions: (i) the near-equilibrium condition and (ii) the positiveness of the entropy production. We explore the range of parameters of the model that allow to fulfill these two conditions at the same time, finding that a viscous WDM component is compatible with both ones, being in this sense, a viable model from the thermodynamic point of view. Furthermore, we constrained the free parameters of the model with the observational data coming from supernovae Ia (SNe Ia) and the observational Hubble parameter data (OHD), using these thermodynamics analyses to define the best priors for the cosmological parameters related to the warmness and the dissipation of the DM, showing that this viscous ΛWDM model can describe the combined SNe Ia+OHD data in the same way as the ΛCDM model. The cosmological constraint at 3σ CL gives us an upper limit on the bulk viscous constant of order ξ0∼106 Pa·s, which is in agreement with some previous investigations. Our results support that the inclusion of a dissipative WDM, as an extension of the standard cosmological model, leads to a both thermodynamically consistent and properly fitted cosmological evolution.

Post-Newtonian non-equilibrium kinetic theory

The post-Newtonian hydrodynamic equations for a non-perfect fluid are developed within the framework of a post-Newtonian Boltzmann equation. The post-Newtonian components of the energy–momentum tensor are determined by considering the relativistic Eckart decomposition for a viscous and heat conducting fluid. From the relativistic Grad distribution function its post-Newtonian expression is derived. The hydrodynamic equations for the mass density, mass-energy density and momentum density are determined from a post-Newtonian transfer equation and Grad’s distribution function. In the non-relativistic limit the Newtonian hydrodynamic equations for mass, momentum and energy densities are recovered.

Microphysical manifestations of viscosity and consequences for anisotropies in the very early universe

It has been known that a non-perfect fluid that accounts for dissipative viscous effects can evade a highly anisotropic chaotic mixmaster approach to a singularity. Viscosity is often simply parameterised in this context, so it remains unclear whether isotropisation can really occur in physically motivated contexts. We present a few examples of microphysical manifestations of viscosity in fluids that interact either gravitationally or, for a scalar field for instance, through a self-coupling term in the potential. In each case, we derive the viscosity coefficient and comment on the applicability of the approximations involved when dealing with dissipative non-perfect fluids. Upon embedding the fluids in a cosmological context, we then show the extent to which these models allow for isotropisation of the universe in the approach to a singularity. We first do this in the context of expansion anisotropy only, i.e., in the case of a Bianchi type-I universe. We then include anisotropic 3-curvature modelled by the Bianchi type-IX metric. It is found that a self-interacting scalar field at finite temperature allows for efficient isotropisation, whether in a Bianchi type-I or type-IX spacetime, although the model is not tractable all the way to a singularity. Mixmaster chaotic behaviour, which is well known to arise in anisotropic models including anisotropic 3-curvature, is found to be suppressed in the latter case as well. We find that the only model permitting an isotropic singularity is that of a dense gas of black holes.

Intrinsically symmetric cosmological model in the presence of dissipative fluids

Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein’s field equations where the spatial sections are flat and the source is a nonperfect fluid such that the dissipative terms can be written in terms of spatial gradients of the energy density under a suitable choice of the coordinate system. It is shown through the calculation of the luminosity distance as a function of the redshift that the presence of such inhomogeneities may lead to an effective deceleration parameter compatible with either the standard [Formula: see text]CDM model or LTB models depending on the choice of boundary conditions with no exotic matter. This fact is another evidence that different inhomogeneous models should be carefully investigated in order to verify which model may be compatible with observations and still be as close as possible to the standard model regarding the underlying assumptions, without resorting necessarily to exotic matter components.

Viscous Ricci dark energy model with matter creation: Exact solution and observational tests

In this paper, the dissipative mechanism (bulk viscosity and matter creation) is introduced to describe the effects of cosmic non-perfect fluid on the Ricci dark energy (RDE) model. We consider matter creation and bulk viscosity as two independent irreversible processes. Assuming suitable forms of the bulk viscous coefficient and matter creation rate, we find the exact solution of the field equations. We carry out fitting analysis on the cosmological parameters in the model by using Type Ia supernovae data, observational Hubble data and baryon acoustic oscillation (BAO) data with cosmic microwave background. We plot the trajectory of cosmological parameters with the best-fit values of model parameters and discuss all possible (deceleration, acceleration and their transitions) evolutions of the model. The current values of deceleration parameter and equation of state parameter are found to be $$q_0=-0.362$$ and $$\omega _{\mathrm {eff}}=-0.575$$ , respectively. The age of the Universe is found to be $$t_0\simeq 13.397$$ Gyr, which is very close to the $$\Lambda $$ CDM model. We further discuss the geometrical diagnostic parameters such as statefinder and Om to distinguish the model with $$\Lambda $$ CDM model. Finally, we discuss the behaviour of energy conditions for our model and find that the model satisfies the null energy condition (NEC), weak energy condition (WEC) and dominant energy condition (DEC) while it violates strong energy condition (SEC).

Causal thermodynamics of a gravitational collapse model for an anisotropic fluid with dissipative flows

This paper presents a hydrodynamic and thermodynamic treatment of a radiant star model that undergoes a dissipative gravitational collapse, from a certain initial configuration until it becomes a black hole. The collapsing star consists of a locally anisotropic non-perfect fluid, where we explore the consequences of including viscous pressures, both shear and bulk viscosities, as well as radial heat flow. We analyze the temporal evolution of the heat flux, mass function, luminosity perceived by an observer at infinity and the effective surface temperature. It is shown that this simple exact model, satisfying all the energy conditions throughout the interior region of the star and during all the collapse process, provides a physically reasonable behavior for the temperature profile in the context of the extended irreversible thermodynamics.

Model-independent reconstruction of the linear anisotropic stress η

In this work, we use recent data on the Hubble expansion rate H(z), the quantity fσ8(z) from redshift space distortions and the statistic Eg from clustering and lensing observables to constrain in a model-independent way the linear anisotropic stress parameter η. This estimate is free of assumptions about initial conditions, bias, the abundance of dark matter and the background expansion. We denote this observable estimator as ηobs. If ηobs turns out to be different from unity, it would imply either a modification of gravity or a non-perfect fluid form of dark energy clustering at sub-horizon scales. Using three different methods to reconstruct the underlying model from data, we report the value of ηobs at three redshift values, z=0.29, 0.58, 0.86. Using the method of polynomial regression, we find ηobs=0.57±1.05, ηobs=0.48±0.96, and ηobs=−0.11±3.21, respectively. Assuming a constant ηobs in this range, we find ηobs=0.49±0.69. We consider this method as our fiducial result, for reasons clarified in the text. The other two methods give for a constant anisotropic stress ηobs=0.15±0.27 (binning) and ηobs=0.53 ± 0.19 (Gaussian Process). We find that all three estimates are compatible with each other within their 1σ error bars. While the polynomial regression method is compatible with standard gravity, the other two methods are in tension with it.

FRW viscous fluid cosmological model with time-dependent inhomogeneous equation of state

In this paper, we present two viscous models of non-perfect fluid by avoiding the introduction of exotic dark energy. We consider the first model in terms of deceleration parameter [Formula: see text] has a viscosity of the form [Formula: see text] and the other model in quadratic form of [Formula: see text] of the type [Formula: see text]. In this framework we find the solutions of field equations by using inhomogeneous equation of state of form [Formula: see text] with equation of state parameter [Formula: see text] is constant and [Formula: see text].

Shear dynamics in higher dimensional FLRW cosmology

We study the shear dynamics of higher dimensional Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) cosmology by considering a non-perfect fluid which exerts different pressure in the normal and extra dimensions. We generalise the definition of shear tensor for higher dimensional space-time and prove it to be consistent with the evolution equation for shear tensor obtained from the Ricci identities. The evolution of shear tensor is investigated numerically. The role of extra dimensions and other parameters involved in shear dynamics is discussed in detail. We find that with increase in anisotropy parameter, time of decay of shear increases while with increase in number of extra dimensions, shear tends to decay early.

Rip/singularity free cosmology models with bulk viscosity

In this paper we present two concrete models of non-perfect fluid with bulk viscosity to interpret the observed cosmic accelerating expansion phenomena, avoiding the introduction of exotic dark energy. The first model we inspect has a viscosity of the form ${\zeta} = {\zeta}_0 + ({\zeta}_1-{\zeta}_2q)H$ by taking into account of the decelerating parameter q, and the other model is of the form ${\zeta} = {\zeta}_0 + {\zeta}_1H + {\zeta}_2H^2$. We give out the exact solutions of such models and further constrain them with the latest Union2 data as well as the currently observed Hubble-parameter dataset (OHD), then we discuss the fate of universe evolution in these models, which confronts neither future singularity nor little/pseudo rip. From the resulting curves by best fittings we find a much more flexible evolution processing due to the presence of viscosity while being consistent with the observational data in the region of data fitting. With the bulk viscosity considered, a more realistic universe scenario is characterized comparable with the {\Lambda}CDM model but without introducing the mysterious dark energy.

Singularities and Entropy in Bulk Viscosity Dark Energy Model

In this paper bulk viscosity is introduced to describe the effects of cosmic non-perfect fluid on the cosmos evolution and to build the unified dark energy (DE) with (dark) matter models. Also we derive a general relation between the bulk viscosity form and Hubble parameter that can provide a procedure for the viscosity DE model building. Especially, a redshift dependent viscosity parameter ζ ∝ λ0 + λ1(1 + z)n proposed in the previous work [X.H. Meng and X. Dou, Commun. Theor. Phys. 52 (2009) 377] is investigated extensively in this present work. Further more we use the recently released supernova dataset (the Constitution dataset) to constrain the model parameters. In order to differentiate the proposed concrete dark energy models from the well known ΛCDM model, statefinder diagnostic method is applied to this bulk viscosity model, as a complementary to the Om parameter diagnostic and the deceleration parameter analysis performed by us before. The DE model evolution behavior and tendency are shown in the plane of the statefinder diagnostic parameter pair {r, s} as axes where the fixed point represents the ΛCDM model. The possible singularity property in this bulk viscosity cosmology is also discussed to which we can conclude that in the different parameter regions chosen properly, this concrete viscosity DE model can have various late evolution behaviors and the late time singularity could be avoided. We also calculate the cosmic entropy in the bulk viscosity dark energy frame, and find that the total entropy in the viscosity DE model increases monotonously with respect to the scale factor evolution, thus this monotonous increasing property can indicate an arrow of time in the universe evolution, though the quantum version of the arrow of time is still very puzzling.

Evolution of Interacting Viscous Dark Energy Model in Einstein Cosmology

We investigate the evolution of the viscous dark energy (DE) interacting with the dark matter (DM) in the Einstein cosmology model. By using the linearizing theory of the dynamical system, we find that, in our model, there exists a stable late time scaling solution which corresponds to the accelerating universe. We also find the unstable solution under some appropriate parameters. In order to alleviate the coincidence problem, some authors considered the effect of quantum correction due to the conform anomaly and the interacting dark energy with the dark matter. However, if we take into account the bulk viscosity of the cosmic fluid, the coincidence problem will be softened just like the interacting dark energy cosmology model. That is to say, both the non-perfect fluid model and the interacting the dark energy cosmic model can alleviate or soften the singularity of the universe.

Bulk Viscous Cosmology: Unified Dark Matter

The bulk viscosity is introduced to model the current observational cosmos and the unified dark matter (dark matter and dark energy). The viscous unified model assumes that the universe is filled with a single nonperfect fluid with a bulk viscosity. We review the general framework for the viscous cosmology model building finding that the Hubble parameter has possessed a direct connection with the bulk viscosity coefficient. For the concrete form of the bulk viscosity, the Hubble parameter which has the scaling relation with the redshift can be obtained generally. We discuss two viscosity models and the cosmological evolution to which they lead in detail. Using SNe Ia data, CMB shift, as well as BAO observations, the viscosity model parameters can be fitted very well. We also briefly review the fitting method in this paper.

General Dynamical Equations for Dingle’s Space-Times Filled with a Charged Non-perfect Fluid

In this paper we have assumed charged non-perfect fluid as the material content of the space-time. The expression for the “mass function-M(r,y,z,t)” is obtained for the general situation and the contributions from the Ricci tensor in the form of material energy density ρ, pressure anisotropy $[\frac{p_{2}+p_{3}}{2}-p_{1}]$ , electromagnetic field energy ℰ and the conformal Weyl tensor, viz. energy density of the free gravitational field e $(=\frac{-3\Psi_{2}}{4\pi})$ are made explicit. This work is an extension of the work obtained earlier by Rao and Hasmani (Math. Today XIIA:71, 1993; New Directions in Relativity and Cosmology, Hadronic Press, Nonantum, 1997) for deriving general dynamical equations for Dingle’s space-times described by this most general orthogonal metric, $$ds^2=\exp(\nu)dt^2-\exp(\lambda)dr^2-\exp(2\alpha)dy^2-\exp(2\beta)dz^2,$$ where ν, λ, α and β are functions of all four space-time variables r, y, z and t.

Friedmann Cosmology with Bulk Viscosity: A Concrete Model for Dark Energy

The universe content is considered as a non-perfect fluid with bulk viscosity and can be described by a general equation of state (endowed some deviation from the conventionally assumed cosmic perfect fluid model). An explicitly bulk viscosity dark energy model is proposed to confront consistently with the current observational data sets by statistical analysis and is shown consistent with (not deviated away much from) the concordant Λ Cold Dark Matter (CDM) model by comparing the decelerating parameter. Also we compare our relatively simple viscosity dark energy model with a more complicated one by contrast with the concordant Λ CDM model and find our model improves for the viscosity dark energy model building. Finally we discuss the perspectives of dark energy probes for the coming years with observations.

Nonconformality and nonperfectness of fluid near phase transition in lattice QCD

We investigate the thermodynamic and transport properties of the real scalar field theory at weak as well as strong couplings in the Hartree approximation of the Cornwall-Jackiw-Tomboulis formalism. To our surprise, we find that near phase transition all the thermodynamic and transport properties of the simplest real scalar model at certain strong coupling agree well with the lattice results of the complex QCD system. We also demonstrate that the system near phase transition is nonconformal and behaves as a nonperfect fluid.

Friedmann Cosmology with a Generalized Equation of State and BulkViscosity

The universe content is considered as a non-perfect fluid withbulk viscosity and is described by a more general equation of state(endowed some deviation from the conventionally assumed cosmicperfect fluid model). We assume the bulk viscosity is a linearcombination of two terms: one is constant, and the other isproportional to the scalar expansion θ = 3ȧ/a. Theequation of state is described as p = (γ−1)ρ+p0, wherep0 is a parameter. In this framework we demonstrate that thismodel can be used to explain the dark energy dominated universe,and different proper choices of the parameters may lead to threekinds of fates of the cosmological evolution: no futuresingularity, big rip, or Type-III singularity as presented in[S. Nojiri, S.D. Odintsov, and S. Tsujikawa, Phys. Rev. D71 (2005) 063004].

Cosmological model with viscosity media (dark fluid) described by an effective equation of state

A generally parameterized equation of state (EOS) is investigated in the cosmological evolution with bulk viscosity media modelled as dark fluid, which can be regarded as a unification of dark energy and dark matter. Compared with the case of the perfect fluid, this EOS has possessed four additional parameters, which can be interpreted as the case of the non-perfect fluid with time-dependent viscosity or the model with variable cosmological constant. From this general EOS, a completely integrable dynamical equation to the scale factor is obtained with its solution explicitly given out. (i) In this parameterized model of cosmology, for a special choice of the parameters we can explain the late-time accelerating expansion universe in a new view. The early inflation, the median (relatively late time) deceleration, and the recently cosmic acceleration may be unified in a single equation. (ii) A generalized relation of the Hubble parameter scaling with the redshift is obtained for some cosmology interests. (iii) By using the SNe Ia data to fit the effective viscosity model we show that the case of matter described by p=0 plus with effective viscosity contributions can fit the observational gold data in an acceptable level.