Barotropic Perfect Fluid Research Articles

5D EChS Cosmology with Perfect Fluid

We consider a Chern-Simons gravity theory in the cosmological context for a flat Friedmann-Robertson-Walker metric in five dimensions, chosen barotropic perfect fluids filled the Universe, that is, an equation of state with constant state parameter for the fluid representing the h field of Einstein-Chern-Simons cosmology and an equation of state with variable state parameter for the fluid representing the matter field.

The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues

AbstractThe Von Mises quasi-linear second order wave equation, which completely describes an irrotational, compressible and barotropic classical perfect fluid, can be derived from a nontrivial least action principle for the velocity scalar potential only, in contrast to existing analog formulations which are expressed in terms of coupled density and velocity fields. In this article, the classicalHamiltonian field theory specifically associated to such an equation is developed in the polytropic case and numerically verified in a simplified situation. The existence of such a mathematical structure suggests new theoretical schemes possibly useful for performing numerical integrations of fluid dynamical equations. Moreover it justifies possible new functional forms for Lagrangian densities and associated Hamiltonian functions in other theoretical classical physics contexts.

Oscillating and static universes from a single barotropic fluid

We consider cosmological solutions to general relativity with a single barotropic fluid, where the pressure is a general function of the density, p = f(ρ). We derive conditions for static and oscillating solutions and provide examples, extending earlier work to these simpler and more general single-fluid cosmologies. Generically we expect such solutions to suffer from instabilities, through effects such as quantum fluctuations or tunneling to zero size. We also find a classical instability (``no-go'' theorem) for oscillating solutions of a single barotropic perfect fluid due to a necessarily negative squared sound speed.

Variable cosmological term Λ ( t ) $\varLambda(t)$

We present the case of time-varying cosmological term $\Lambda(t)$. The main idea arises by proposing that as in the cosmological constant case, the scalar potential is identified as $ V(\phi)=2\Lambda$, with $\Lambda$ a constant, this identification should be kept even when the cosmological term has a temporal dependence, i.e., $ V(\phi(t))=2\Lambda(t)$. We Use the Lagrangian formalism for a scalar field $\phi$ with standard kinetic energy and arbitrary potential $V(\phi)$ and apply this model to the Friedmann-Robertson-Walker (FRW)cosmology. Exact solutions of the field equations are obtained by a special ansatz to solve the Einstein-Klein-Gordon equation and a particular potential for the scalar field and barotropic perfect fluid. We present the evolution on this cosmological term with different scenarios.

Time-varying cosmological term

We present the case of time-varying cosmological term using the Lagrangian formalism characterized by a scalar field ϕ with standard kinetic energy and arbitrary potential V(ϕ). This model is applied to Friedmann-Robertson-Walker (FRW)cosmology. Exact solutions of the field equations are obtained by a special ansats to solve the Einstein-Klein-Gordon equation and a particular potential for the scalar field and barotropic perfect fluid. We present the evolution on this cosmological term with different scenarios.

The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier

We show that very general scalar-tensor theories of gravity (including, e.g., Horndeski models) are generically invariant under disformal transformations. However there is a special subset, when the transformation is not invertible, that yields new equations of motion which are a generalization of the so-called “mimetic” dark matter theory recently introduced by Chamsedinne and Mukhanov. These conclusions hold true irrespective of whether the scalar field in the action of the assumed scalar-tensor theory of gravity is the same or different than the scalar field involved in the transformation. The new equations of motion for our general mimetic theory can also be derived from an action containing an additional Lagrange multiplier field. The general mimetic scalar-tensor theory has the same number of derivatives in the equations of motion as the original scalar-tensor theory. As an application we show that the simplest mimetic scalar-tensor model is able to mimic the cosmological background of a flat FLRW model with a barotropic perfect fluid with any constant equation of state.

Observational signatures of the theories beyond Horndeski

In the approach of the effective field theory of modified gravity, we derive the equations of motion for linear perturbations in the presence of a barotropic perfect fluid on the flat isotropic cosmological background. In a simple version of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, which is the minimum extension of Horndeski theories, we show that a slight deviation of the tensor propagation speed squared ct2 from 1 generally leads to the large modification to the propagation speed squared cs2 of a scalar degree of freedom ϕ. This problem persists whenever the kinetic energy ρX of the field ϕ is much smaller than the background energy density ρm, which is the case for most of dark energy models in the asymptotic past. Since the scaling solution characterized by the constant ratio ρX/ρm is one way out for avoiding such a problem, we study the evolution of perturbations for a scaling dark energy model in the framework of GLPV theories in the Jordan frame. Provided the oscillating mode of scalar perturbations is fine-tuned so that it is initially suppressed, the anisotropic parameter η=−Φ/Ψ between the two gravitational potentials Ψ and Φ significantly deviates from 1 for ct2 away from 1. For other general initial conditions, the deviation of ct2 from 1 gives rise to the large oscillation of Ψ with the frequency related to cs2. In both cases, the model can leave distinct imprints for the observations of CMB and weak lensing.

Noncommutative Quantum Anisotropic cosmology in K-essence

We study a canonical noncommutative extension of the Bianchi type I Minisuperspace, with a barotropic perfect fluid, in the context of a simplified form of k-essence known as the Sáez-Ballester theory. Noncommutativity is implemented in the pure gravitational sector. The corresponding noncommutative Wheeler-DeWitt equation is constructed and solved. Quantum solutions are obtained for any value of the barotropic parameter. It is seen that the effect of this particular noncommutativity is that of modulating the amplitude of the commutative wave function.

Anisotropic cosmology in K-essence theory

We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid (p = γρ) modeling the usual matter content and include the particular form of potential V(ϕ) = constant = 2Λ. The classical solutions for any γ ≠ 1 and Λ = 0 are found in closed form, using a time transformation. We also present the solution when Λ ≠ 0 including particular values in the barotropic parameter. We present the possible isotropization of the cosmological model Bianchi I using the ratio between the anisotropic parameters and the volume of the universe and show that this tend to a constant or to zero for different cases.

Cosmological scaling solutions for multiple scalar fields

The general k-essence Lagrangian for the existence of cosmological scaling solutions is derived in the presence of multiple scalar fields coupled to a barotropic perfect fluid. In addition to the scaling fixed point associated with the dynamics during the radiation and matter eras, we also obtain a scalar-field dominated solution relevant to dark energy and discuss the stability of them in the two-field set-up. We apply our general results to a model of two canonical fields with coupled exponential potentials arising in string theory. Depending on model parameters and initial conditions, we show that the scaling matter-dominated epochs followed by an attractor with cosmic acceleration can be realized with/without the couplings to scalar fields. The different types of scaling solutions can be distinguished from each other by the evolution of the dark energy equation of state from high-redshifts to today.

Quantum Bianchi Type IX Cosmology in K-Essence Theory

We use one of the simplest forms of the K-essence theory and apply it to the anisotropic Bianchi type IX cosmological model, with a barotropic perfect fluid modeling the usual matter content. We show that the most important contribution of the scalar field occurs during a stiff matter phase. Also, we present a canonical quantization procedure of the theory which can be simplified by reinterpreting the scalar field as an exotic part of the total matter content. The solutions to the Wheeler-DeWitt equation were found using the Bohmian formulation Bohm (Phys. Rev. 85(2):166, 1952) of quantum mechanics, employing the amplitude-real-phase approach Moncrief and Ryan (Phys. Rev. D 44:2375, 1991), where the ansatz for the wave function is of the form Ψ(lμ)=χ(ϕ)W(lμ)\(e^{- S(\ell ^{\mu })},\), where S is the superpotential function, which plays an important role in solving the Hamilton-Jacobi equation.

Qualitative analysis of collapsing isotropic fluid spacetimes

The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us, under a hypothesis of Taylor-expandability with respect to one of the coordinates, to approach the problem of the nature of the final state without knowing explicitly the metric. The method is applied to investigate the singularities of linear barotropic perfect fluids solutions and to a family of accelerating fluids.

Classical Bianchi Type I Cosmology in K-Essence Theory

We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid (p=γρ) modeling the usual matter content and with cosmological constantΛ. Classical exact solutions for anyγ≠1andΛ=0are found in closed form, whereas solutions forΛ≠0are found for particular values in the barotropic parameter. We present the possible isotropization of the cosmological model Bianchi I using the ratio between the anisotropic parameters and the volume of the universe. We also include a qualitative analysis of the analog of the Friedmann equation.

Non-static plane symmetric massive string magnetized perfect fluid cosmological models in bimetric theory of gravitation

In this paper,we investigate the non-static massive string magnetized barotropic perfect fluid cosmological models in Rosen's (Gen.Rel.Grav.Vol.4 (1973) 435) bimetric theory of gravitation. Using the relation isotropic pressure 'p' directly proportional to energy density 'ρ' ( i.e p = Є1 ρ , where -1 ≤ Є1 ≤ 1) , dust filled geometric string model and stiff fluid filled model of the universe are obtained. Some physical and geometrical behavior of the exhibited models are also discussed.

Fluid inflation

In this work we present an inflationary mechanism based on fluid dynamics. Starting with the action for a single barotropic perfect fluid, we outline the procedure to calculate the power spectrum and the bispectrum of the curvature perturbation. It is shown that a perfect barotropic fluid naturally gives rise to a non-attractor inflationary universe in which the curvature perturbation is not frozen on super-horizon scales. We show that a scale-invariant power spectrum can be obtained with the local non-Gaussianity parameter fNL = 5/2.

THE DYNAMICS OF TACHYON FIELD WITH AN INVERSE SQUARE POTENTIAL IN LOOP QUANTUM COSMOLOGY

The dynamical behavior of tachyon field with an inverse potential is investigated in loop quantum cosmology. It reveals that the late-time behavior of tachyon field with this potential leads to a power-law expansion. In addition, an additional barotropic perfect fluid with the adiabatic index 0 < γ < 2 is added and the dynamical system is shown to be an autonomous one. The stability of this autonomous system is discussed using phase plane analysis. There exist up to five fixed points with only two of them possibly stable. The two stable node (attractor) solutions are specified and their cosmological indications are discussed. For the tachyon dominated solution, the further discussion is stretched to the possibility of considering tachyon field as a combination of two parts which respectively behave like dark matter and dark energy.

Reconstruction of scalar potentials in modified gravity models

We employ the superpotential technique for the reconstruction of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the Hubble parameter is considered as a function of the scalar field, and this allows one to reconstruct the scalar field potential and determine the dynamics of the field itself, without a priori fixing the Hubble parameter as a function of time or of the scale factor. The scalar field potentials that lead to de Sitter or asymptotic de Sitter solutions, and those that reproduce the cosmological evolution given by Einstein-Hilbert action plus a barotropic perfect fluid, have been obtained.

Classical field theory of the Von Mises equation for irrotational polytropic inviscid fluids

The Von Mises second-order quasi-linear partial differential equation describes the dynamics of an irrotational, compressible and barotropic classical perfect fluid through a scalar function only, i.e. the velocity potential. It is shown here how to derive it in the case of a polytropic equation of state starting from a least action principle. The Lagrangian density is found to coincide with pressure. Once re-expressed in terms of the velocity potential, the action integral presents some similarities with other classical and quantum field theories. Aided by the Legendre transformation tool, we show that the nonlinear equation is completely integrable in the case of a non-steady parallel flow dynamics. A numerical solution of the equation in a critical shock wave forming scenario allows one to analyze then such a particular dynamics by using the so-called analogue gravity formalism which impressively links ordinary perfect fluids to curved spacetimes. Finally, implications for fluid dynamics and field theories are discussed.

Canonical and phantom scalar fields as an interaction of two perfect fluids

In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $\rho_1(t)$ with a stiff equation of state ($p_1=\rho_1$), and an "effective vacuum energy" $\rho_2(t)$ with a cosmological constant equation of state ($p_2=-\rho_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies is that it gives, by choosing a suitable form of the interacting term $Q$, an approach for obtaining exact and numerical solutions. The choice of $Q$ merely determines a specific scalar field with its potential, thus allowing to generate closed, open and flat FRW scalar field cosmologies.

New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state

In this paper we give a simple proof that when the particle number is conserved, the Lagrangian of a barotropic perfect fluid is ${\mathcal{L}}_{m}=\ensuremath{-}\ensuremath{\rho}[{c}^{2}+\ensuremath{\int}P(\ensuremath{\rho})/{\ensuremath{\rho}}^{2}d\ensuremath{\rho}]$, where $\ensuremath{\rho}$ is the rest mass density and $P(\ensuremath{\rho})$ is the pressure. To prove this result, neither additional fields nor Lagrange multipliers are needed. Besides, the result is applicable to a wide range of theories of gravitation. The only assumptions used in the derivation are: 1) the matter part of the Lagrangian does not depend on the derivatives of the metric, and 2) the particle number of the fluid is conserved (${\ensuremath{\nabla}}_{\ensuremath{\sigma}}(\ensuremath{\rho}{u}^{\ensuremath{\sigma}})=0$).