Imperfect Fluid Research Articles

Backreaction mechanism in multifluid and extended cosmologies

One possible explanation for the present observed acceleration of the Universe is the breakdown of homogeneity and isotropy due to the formation of non-linear structures. How inhomogeneities affect the averaged cosmological expansion rate and lead to late-time acceleration is generally considered to be due to some backreaction mechanism.In the recent literature most averaging calculations have focused their attention on General Relativity together with pressure-free matter.In this communication we focus our attention on more general scenarios, including imperfect fluids as well as alternative theories of gravity, and apply an averaging procedure to them in order to determine possible backreaction effects. For illustrative purposes, we present our results for dark energy models, quintessence and Brans-Dicke theories. We also provide a discussion about the limitations of frame choices in the averaging procedure.

Emergent Quantum Euler Equation and Bose–Einstein Condensates

In this paper, proceeding from the recently developed way of deriving the quantum-mechanical equations from the classical ones, the complete system of hydrodynamical equations, including the quantum Euler equation, is derived for a perfect fluid and an imperfect fluid with pairwise interaction between the particles. For the Bose-Einstein condensate of the latter one the Bogolyubov spectrum of elementary excitations is easily reproduced in the acoustic approximation.

Bose–Einstein condensate dark matter phase transition from finite temperature symmetry breaking of Klein–Gordon fields

In this paper, the thermal evolution of scalar field dark matter (SFDM) particles at finite cosmological temperatures is studied. Starting with a real SF in a thermal bath and using the one-loop quantum corrections potential, we rewrite Klein–Gordon’s equation in its hydrodynamical representation and study the phase transition of this SF due to a Z2 symmetry breaking of its potential. A very general version of a nonlinear Schrödinger equation is obtained. When introducing Madelung’s representation, the continuity and momentum equations for a non-ideal SFDM fluid are formulated, and the cosmological scenario with the SFDM described in analogy to an imperfect fluid is then considered where dissipative contributions are obtained in a natural way. Additional terms appear in the results compared to those in the classical version commonly used to describe the ΛCDM model, i.e., the ideal fluid. The equations and parameters that characterize the physical properties of the system such as its energy, momentum and viscous flow are related to the temperature of the system, scale factor, Hubble’s expansion parameter and the matter energy density. Finally, some details on how galaxy halos and smaller structures might be able to form by condensation of this SF are given.

Regular and conformal regular cores for static and rotating solutions

Using a new metric for generating rotating solutions, we derive in a general fashion the solution of an imperfect fluid and that of its conformal homolog. We discuss the conditions that the stress–energy tensors and invariant scalars be regular. On classical physical grounds, it is stressed that conformal fluids used as cores for static or rotating solutions are exempt from any malicious behavior in that they are finite and defined everywhere.

Interacting viscous dark fluids

We revise the conditions for the physical viability of a cosmological model in which dark matter has bulk viscosity and also interacts with dark energy. We have also included radiation and baryonic matter components; all matter components are represented by perfect fluids, except the dark matter, that is treated as an imperfect fluid. We impose upon the model the condition of a complete cosmological dynamics that results in an either null or negative bulk viscosity, but the latter also disagrees with the Local Second Law of Thermodynamics. The model is also compared with cosmological observations at different redshifts: type Ia supernova, the shift parameter of CMB, the acoustic peak of BAO, and the Hubble parameter H(z). In general, observations consistently point out to a negative value of the bulk viscous coefficient, and in overall the fitting procedure shows no preference for the model over the standard LCDM model.

A NONSINGULAR PERFECT FLUID CLASSICAL LEPTON MODEL OF ARBITRARILY SMALL RADIUS

We exhibit a classical lepton model based on a perfect fluid that reproduces leptonic charges and masses in arbitrarily small volumes without metric singularities or pressure discontinuities. This solution is the first of this kind to our knowledge, because to date the only classical general relativistic models that have reproduced leptonic charges and masses in arbitrarily small volumes are based on imperfect (anisotopic) fluids or perfect fluids with electric field discontinuities. We use a Maxwell–Einstein exact metric for a spherically symmetric static perfect fluid in a region in which the pressure vanishes at a boundary, beyond which the metric is of the Reissner–Nordström form. This construction models lepton mass and charge in the limit as the boundary → 0.

Electromagnetic field and dynamics of tilted Lemaitre-Tolman-Bondi spacetimes

In this paper, we investigate the dynamics of Lemaitre-Tolman-Bondi spacetimes with imperfect fluid in the presence of electromagnetic field. We study the effects of charge with respect to an observer moving radially relative to the fluid, that is, a tilted observer. The relationship between various quantities in the tilted and non-tilted congruences is developed using the Einstein-Maxwell field equations. We explore various factors affecting the inhomogeneities in the energy density of the fluid and also discuss the stability of the non-tilted congruence.

Bianchi Type-III Cosmological Models with Anisotropic Dark Energy (DE) in Lyra Geometry

The main purpose of this paper is to explore the solutions of Bianchi type-III cosmological model in Lyra geometry in the background of anisotropic dark energy. The general form of the anisotropy parameter of the expansion for Bianchi type-III space time is obtained in the presence of a single imperfect fluid with a dynamical anisotropic equation of state parameter and a dynamical energy density in Lyra geometry. A special law is assumed for the anisotropy of the fluid with reduces the anisotropy parameter of the expansion to a simple form \(\Delta \propto \frac{1}{H^{2}V^{2}}\). The exact solutions of the field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power law volumetric expansion. The isotropy of the fluid, space and expansion are discussed. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models. The expression for the look-back time, proper distance, luminosity distance and angular diameter distance are also derived.

On the conformal version of Schwarzschild – de Sitter spacetime

An imperfect cosmic fluid with energy flux is analyzed. Even though its energy density ρ is positive, the pressure p = −ρ due to the fact that the metric is asymptotically de Sitter. The kinematical quantities for a nongeodesic congruence are computed. The scalar expansion is time independent but divergent at the singularity r = 2m. Far from the central mass m and for a cosmic time t̄ << H−1, the heat flux q does not depend on Newton's constant G.

DOES PRESSURE ACCENTUATE GENERAL RELATIVISTIC GRAVITATIONAL COLLAPSE AND FORMATION OF TRAPPED SURFACES?

It is widely believed that though pressure resists gravitational collapse in Newtonian gravity, it aids the same in general relativity (GR) so that GR collapse should eventually be similar to the monotonous free fall case. But we show that, even in the context of radiationless adiabatic collapse of a perfect fluid, pressure tends to resist GR collapse in a manner which is more pronounced than the corresponding Newtonian case and formation of trapped surfaces is inhibited. In fact there are many works which show such collapse to rebound or become oscillatory implying a tug of war between attractive gravity and repulsive pressure gradient. Furthermore, for an imperfect fluid, the resistive effect of pressure could be significant due to likely dramatic increase of tangential pressure beyond the "photon sphere." Indeed, with inclusion of tangential pressure, in principle, there can be static objects with surface gravitational redshift z → ∞. Therefore, pressure can certainly oppose gravitational contraction in GR in a significant manner in contradiction to the idea of Roger Penrose that GR continued collapse must be unstoppable.

Consistent perturbations in an imperfect fluid

We present a new prescription for analysing cosmological perturbationsin a more-general class of scalar-field dark-energy models where theenergy-momentum tensor has an imperfect-fluid form. This class includesBrans-Dicke models, f(R) gravity, theories with kinetic gravitybraiding and generalised galileons. We employ the intuitive languageof fluids, allowing us to explicitly maintain a dependence on physicaland potentially measurable properties. We demonstrate that hydrodynamicsis not always a valid description for describing cosmological perturbationsin general scalar-field theories and present a consistent alternativethat nonetheless utilises the fluid language.We apply this approach explicitly to a worked example: k-essencenon-minimally coupled to gravity. This is the simplest case whichcaptures the essential new features of these imperfect-fluid models.We demonstrate the generic existence of a new scale separating regimeswhere the fluid is perfect and imperfect. We obtain the equationsfor the evolution of dark-energy density perturbations in both theseregimes. The model also features two other known scales: the Comptonscale related to the breaking of shift symmetry and the Jeans scalewhich we show is determined by the speed of propagation of small scalar-fieldperturbations, i.e. causality, as opposed to the frequently used definitionof the ratio of the pressure and energy-density perturbations.

Testing for dynamical dark energy models with redshift-space distortions

The red-shift space distortions in the galaxy power spectrum can be used to measure the growth rate of matter density perturbations δm.For dynamical dark energy models in General Relativitywe provide a convenient analytic formula of f(z)σ8(z)written as a function of the redshift z, where f = dln δm/dln a(a is the cosmological scale factor) and σ8 is the rms amplitude of over-density at the scale 8 h−1 Mpc.Our formula can be applied to the models of imperfect fluids, quintessence, and k-essence, provided that the dark energy equation of state w does not vary significantly and that the sound speed is not much smaller than 1.We also place observational constraints on dark energy modelsof constant w and tracking quintessence from the recent data of red-shift space distortions.

Realistic fluids as source for dynamically accreting black holes in a cosmological background

We show that a single imperfect fluid can be used as a source to obtain the generalized McVittie metric as an exact solution to Einstein's equations. The mass parameter in this metric varies with time thanks to a mechanism based on the presence of a temperature gradient. This fully dynamical solution is interpreted as an accreting black hole in an expanding universe if the metric asymptotes to Schwarzschild-de Sitter at temporal infinity. We present a simple but instructive example for the mass function and briefly discuss the structure of the apparent horizons and the past singularity.

Turbulence and little rip cosmology

A variety of conditions are considered under which the cosmic dark fluid may be able to develop a future Big Rip or Little Rip singularity. Both one-component and two-component models are considered. In the latter case we present a way in which the fluid can be decomposed into two components, one nonturbulent (ideal) and one turbulent part, obeying two different equations of state. For the nonturbulent part, the thermodynamical parameter, commonly called $w$, is assumed to be less than $\ensuremath{-}1$ throughout. For the turbulent part, it turns out that it is sufficient that ${w}_{\mathrm{turb}}$ lies in the quintessence region in order to lead to a singularity. Both Big Rip and Little Rip behavior for dark energy are found. In the one-component case, we examine how the universe may develop from a viscous era with constant bulk viscosity into a turbulent era, the turbulence in effect protecting the universe from encountering the singularity at all. The equivalent description of the same cosmology in terms of inhomogeneous (imperfect) fluid is also presented.

Vorticity and entropy production in tilted Szekeres spacetimes

We analyze the properties of the tilted Szekeres spacetime, i.e. the version of such spacetime as seen by a congruence of observers with respect to which the fluid is moving. The imperfect fluid and the kinematical variables associated to the four-velocity of the fluid assigned by tilted observers are studied in detail. As it happens for the case of the Lemaitre--Tolman--Bondi spacetime, the fluid evolves nonreversibly (with nonvanishing entropy production) and is nongeodesic. However unlike that later case, the tilted observer detects vorticity in the congruence of the fluid world lines. Also, as for the nontilted congruence the magnetic part of the Weyl tensor vanishes, reinforcing the nonradiative character of this kind of spacetime. Possible physical implications of these results are discussed.

Non-adiabatic radiative collapse of a relativistic star under different initial conditions

We examine the role of space-time geometry in the non-adiabatic collapse of a star dissipating energy in the form of radial heat flow, studying its evolution under different initial conditions. The collapse of a star filled with a homogeneous perfect fluid is compared with that of a star filled with inhomogeneous imperfect fluid under anisotropic pressure. Both the configurations are spherically symmetric. However, in the latter case, the physical space t = constant of the configurations endowed with spheroidal or pseudospheroidal geometry is assumed to be inhomogeneous. It is observed that as long as the collapse is shear-free, its evolution depends only on the mass and size of the star at the onset of collapse.

On dark energy models of single scalar field

In this paper we revisit the dynamical dark energy model building based on single scalar field involving higher derivative terms. By imposing a degenerate condition on the higher derivatives in curved spacetime, one can select the models which are free from the ghost mode and the equation of state is able to cross the cosmological constant boundary smoothly, dynamically violate the null energy condition. Generally the Lagrangian of this type of dark energy models depends on the second derivatives linearly. It behaves like an imperfect fluid, thus its cosmological perturbation theory needs to be generalized. We also study such a model with explicit form of degenerate Lagrangian and show that its equation of state may cross -1 without any instability.

Reversible dissipative processes, conformal motions and Landau damping

The existence of a dissipative flux vector is known to be compatible with reversible processes, provided a timelike conformal Killing vector (CKV) χα=VαT (where Vα and T denote the four-velocity and temperature respectively) is admitted by the spacetime. Here we show that if a constitutive transport equation, either within the context of standard irreversible thermodynamics or the causal Israel–Stewart theory, is adopted, then such a compatibility also requires vanishing dissipative fluxes. Therefore, in this later case the vanishing of entropy production generated by the existence of such CKV is not actually associated to an imperfect fluid, but to a non-dissipative one. We discuss also about Landau damping.

The imperfect fluid behind kinetic gravity braiding

We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current. The fluid has zero vorticity and is not dissipative: there is no entropy production, the energy-momentum is exactly conserved, the temperature vanishes and there is no shear viscosity. Still, in an expansion around a perfect fluid one can identify terms which correct the pressure in the manner of bulk viscosity. We close by formulating the non-trivial conditions for the thermodynamic equilibrium of this imperfect fluid.

A nonsingular cosmological model with shear and rotation

We have investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large value of time.