Form Of Perfect Fluid Research Articles

TDiff in the dark: gravity with a scalar field invariant under transverse diffeomorphisms

We reflect on the possibility of having a matter action that is invariant only under transverse diffeomorphisms. This possibility is particularly interesting for the dark sector, where no restrictions arise based on the weak equivalence principle. In order to implement this idea we consider a scalar field which couples to gravity minimally but via arbitrary functions of the metric determinant. We show that the energy-momentum tensor of the scalar field takes the perfect fluid form when its velocity vector is time-like. We analyze the conservation of this tensor in detail, obtaining a seminal novel result for the energy density of this field in the kinetic dominated regime. Indeed, in this regime the fluid is always adiabatic and we obtain an explicit expression for the speed of sound. Furthermore, to get insight in the gravitational properties of these theories, we consider the fulfillment of the energy conditions, concluding that nontrivial physically reasonable matter violates the strong energy condition in the potential domination regime. On the other hand, we present some shift-symmetric models of particular interest. These are: constant equation of state models (which may provide us with a successful description of dark matter or dark radiation) and models presenting different gravitational domains (characterized by the focusing or possible defocusing of time-like geodesics), as it happens in unified dark matter-energy models.

A note on generalized weakly ℋ-symmetric manifolds and relativistic applications

In this work, generalized weakly [Formula: see text]-symmetric space-times [Formula: see text] are investigated, where [Formula: see text] is any symmetric [Formula: see text] tensor. It is proved that, in a nontrivial [Formula: see text] space-time, the tensor [Formula: see text] has a perfect fluid form. Accordingly, sufficient conditions for a nontrivial generalized weakly Ricci symmetric space-time [Formula: see text] to be either an Einstein space-time or a perfect fluid space-time are obtained. Also, conditions for space-times admitting either a generalized weakly symmetric energy-momentum tensor or a generalized weakly symmetric [Formula: see text] tensor to be Einstein or perfect fluid space-times are provided.

A Note on Generalized Quasi-Einstein and (λ, n + m)-Einstein Manifolds with Harmonic Conformal Tensor

Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M,g,f,μ to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a λ,n+m-Einstein manifold M,g,w having harmonic Weyl tensor, ∇jw∇mwCjklm=0 and ∇lw∇lw<0 reduces to a perfect fluid generalized Robertson–Walker spacetime with Einstein fibers. Finally, M,g,w reduces to a perfect fluid manifold if φ=−m∇lnw is a φRic-vector field on M and to an Einstein manifold if ψ=∇w is a ψRic-vector field on M. Some consequences of these results are considered.

Carroll Symmetry, Dark Energy and Inflation

Carroll symmetry arises from Poincaré symmetry upon taking the limit of vanishing speed of light. We determine the constraints on the energy-momentum tensor implied by Carroll symmetry and show that for energy-momentum tensors of perfect fluid form, these imply an equation of state E+P=0 for energy density plus pressure. Therefore Carroll symmetry might be relevant for dark energy and inflation. In the Carroll limit, the Hubble radius goes to zero and outside it recessional velocities are naturally large compared to the speed of light. The de Sitter group of isometries, after the limit, becomes the conformal group in Euclidean flat space. We also study the Carroll limit of chaotic inflation, and show that the scalar field is naturally driven to have an equation of state with w = − 1. Finally we show that the freeze-out of scalar perturbations in the two point function at horizon crossing is a consequence of Carroll symmetry. To make the paper self-contained, we include a brief pedagogical review of Carroll symmetry, Carroll particles and Carroll field theories that contains some new material as well. In particular we show, using an expansion around speed of light going to zero, that for scalar and Maxwell type theories one can take two different Carroll limits at the level of the action. In the Maxwell case these correspond to the electric and magnetic limit. For point particles we show that there are two types of Carroll particles: those that cannot move in space and particles that cannot stand still.

Dynamical system analysis of logotropic dark fluid with a power law in the rest-mass energy density

We consider a spatially flat FLRW universe. We assume that it is filled with dark energy in the form of logotropic dark fluid coupled with dark matter in the form of a perfect fluid having a barotropic equation of state. We employ dynamical system tools to obtain a complete qualitative idea of the evolution of such a universe. It is interesting to note that we ought to consider an approximation for the pressure of the logotropic dark fluid in the form of an infinite series so as to be able to construct the autonomous system required for a dynamical system study. This series form provides us with a power law in the rest-mass energy density of the logotropic dark fluid. We compute the critical points of the autonomous system and analyze these critical points by applying linear stability theory. Our analysis reveal a scenario of late-time accelerated universe dominated by the logotropic fluid which behaves as cosmological constant, preceded by an intermediate phase of the Universe dominated by logotropic fluid which behaves as dark matter in the form of perfect fluid. Moreover, it also crosses the phantom divide line.

Panorama behaviors of general relativistic hydrodynamics and holographic dark energy in [formula omitted] gravity

The main motive of this study is to investigate behaviors of general relativistic hydrodynamics in the form of perfect fluid and holographic dark energy for anisotropic and homogenous space-time in the framework of f(R,T) gravity. The field equations are solved using (i) the shear scalar of the metric is proportional to the expansion scalar which results a relationship between metric potentials and (ii) special law of variation of Hubble's parameter (Berman (1983)) that yields constant deceleration parameter. The cosmological parameters like energy density, EoS parameter, statefinder parameters, jerk parameter, thermodynamic temperatures and entropy densities of the models are obtained and discussed their physical significance in the light of the recent scenario of accelerated expansion of the universe and cosmological observations. The well-known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (dL) and distance modulus μ(z)with redshift are studied.

Scalar and vector perturbations in a universe with nonlinear perfect fluid

We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.

Cosmological perfect fluids in higher-order gravity

We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian density $F(R,\square R, ... , \square^k R)$ have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.

Interacting dark energy model in the brane scenario: A dynamical system analysis

The present work is a second in the series of investigations of the background dynamics in brane cosmology when dark energy is coupled to dark matter by a suitable interaction. Here, dark matter is chosen in the form of perfect fluid with barotropic equation of state, while a real scalar field with self-interacting potential is chosen as dark energy. The scalar field potential is chosen as exponential or hyperbolic in nature and three different choices for the interactions between the dark species are considered. In the background of spatially flat, homogeneous and isotropic Friedmann–Robertson–Walker (FRW) brane model, the evolution equations are reduced to an autonomous system by suitable transformation of variables and a series of critical points are obtained for different interactions. By analyzing the critical points, we have found a cosmologically viable model describing an early inflationary scenario to dark energy-dominated era connecting through a matter-dominated phase.

Perfect-fluid, generalized Robertson-Walker space-times, and Gray’s decomposition

We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In all but one, the Ricci tensor is Einstein or has the form of perfect fluid. We discuss the corresponding equations of state that result from the Einstein equation in dimension 4, where perfect-fluid GRW space-times are Robertson-Walker.

Scalar perturbations in cosmological f(R) models: the cosmic screening approach

We investigate cosmological perturbations for nonlinear f(R) models within the cosmic screening approach. Matter is considered both in the form of a set of discrete point-like massive bodies and in the form of a continuous pressureless perfect fluid. We perform full relativistic analysis of the first-order theory of scalar perturbations for arbitrary nonlinear f(R) models and demonstrate that scalar potentials {varPhi }(t,{mathbf {r}}) and {varPsi }(t,{mathbf {r}}) are determined by a system of only two master equations. Our equations are applicable at all spatial scales as long as the approximation delta R/{bar{R}} ll 1 (which is usually assumed in studies devoted to cosmological perturbations in f(R) models) works.

Does particle creation mechanism favour formation of black hole or naked singularity?

The paper deals with collapse dynamics of a spherically symmetric massive star in the framework of non-equilibrium thermodynamic prescription through particle creation mechanism. The matter content in the star is in the form of perfect fluid with barotropic equation of state, and the dissipative phenomena due to non-equilibrium thermodynamics is in the form of bulk viscosity. For simplicity, the thermodynamic system is chosen to be adiabatic so that the effective bulk viscous pressure is linearly related to the particle creation rate. As a result, the evolution of the collapsing star also depends on the particle creation rate. By proper choice of creation rate as a function of the Hubble parameter, it is found that the end state of the collapse may be either a black hole (BH) or a naked singularity (NS).

Anisotropic Behavior of Cosmological Models with Exponential and Hyperbolic Scale Factors

In this paper, the cosmological models of the universe are constructed in gravity with choice of the functional in the form and . The space-time considered here is Bianchi Type I and the energy momentum tensor is in the form of perfect fluid. Two cosmological models are presented using a power form of exponential function and a hyperbolic form. The energy conditions along with the state finder diagnostic pair have been obtained and analyzed.

Cylindrically symmetric cosmological model of the universe in modified gravity

In this paper, we have constructed the cosmological models of the universe in a cylindrically symmetric space time in two classes of \(f(R,T)\) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011). We have discussed two cases: one in the linear form and the other in the quadratic form of \(R\). The matter is considered to be in the form of perfect fluid. It is observed that in the first case, the pressure and energy density remain the same, which reduces to a Zeldovich fluid. In the second case we have studied the quadratic function of \(f(R,T)\) gravity in the form \(f(R)=\lambda(R+R^{2})\) and \(f(T)=\lambda T\). In the second case the pressure is in the negative domain and the energy density is in the positive domain, which confirms that the equation of state parameter is negative. The physical properties of the constructed models are studied.

A dynamical system analysis of f(R,T) gravity

We investigate equations of motion and future singularities of [Formula: see text] gravity where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. We also investigate [Formula: see text] gravity by the method of dynamical systems and obtain some fixed points. Finally, the effect of the Noether symmetry on [Formula: see text] is studied and the consistent form of [Formula: see text] function is found using the symmetry and the conserved charge.

K-essence model from the mechanical approach point of view: coupled scalar field and the late cosmic acceleration

In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, we can consider the Universe to be filled with dust-like matter in the form of discretely distributed galaxies, a K-essence scalar field, playing the role of dark energy, and radiation as matter sources. We investigate such a Universe in the mechanical approach. This means that the peculiar velocities of the inhomogeneities (in the form of galaxies) as well as the fluctuations of the other perfect fluids are non-relativistic. Such fluids are designated as coupled because they are concentrated around the inhomogeneities. In the present paper, we investigate the conditions under which the K-essence scalar field with the most general form for its action can become coupled. We investigate at the background level three particular examples of the K-essence models: (i) the pure kinetic K-essence field, (ii) a K-essence with a constant speed of sound and (iii) the K-essence model with the Lagrangian bX+cX2−V(ϕ). We demonstrate that if the K-essence is coupled, all these K-essence models take the form of multicomponent perfect fluids where one of the component is the cosmological constant. Therefore, they can provide the late-time cosmic acceleration and be simultaneously compatible with the mechanical approach.

Non-static cosmological model in f ( R , T ) $f(R,T)$ gravity

In this paper, we have studied the Einstein-Rosen space time in $f(R,T)$ gravity by considering the second model of Harko et al. (Phys. Rev. D 84:024020, 2011), $f(R,T) = f_{1}(R)+f_{2}(T)$ , where $f_{1}(R)=\lambda R$ ; $f_{2}(T)=\lambda T$ and $f_{1}(R)=\lambda R$ ; $f_{2}(T)=\lambda T^{2}$ . The matter field is considered in the form of perfect fluid. It is observed that, the perfect fluid represent the Zel’dovich universe in both the forms.

Rotating thin shells in (2 + 1)-dimensional asymptotically AdS spacetimes: Mechanical properties, machian effects, and energy conditions

In this paper, a rotating thin shell in a (2 + 1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2 + 1) dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy–density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy–momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2 + 1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.

Non-existence of perfect dark energy fluid in Bianchi type-IV space time

In this paper, non-diagonal Bianchi type-IV space-time is investigated in Einstein general theory of relativity. The matter field is considered in the form of perfect dark energy fluid. It is interesting to observe that in this case, Bianchi type IV perfect dark energy fluid cosmological model does not exist. The space-time reduces to Minkowskian geometry.

DARK ENERGY COSMOLOGICAL MODEL FOR BIANCHI TYPE III SPACE-TIME WITH PERFECT FLUID

In this paper, the problem of diagonal Bianchi type III space-time is investigated in scale invariant theory with dark energy. The matter field is considered in the form of perfect fluid. The field equations for scale invariant theory has been solved by applying a variation law for generalized Hubble's parameter (Nuovo Cimento B 74:182, 1983). The gauge function depends on time coordinate only (Dirac gauge). The cosmological model is constructed, its physical and kinematical properties are discussed.