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A kinetic theory for moderately dense gases of inelastic and rough spherical molecules is developed from the Enskog equation where a macroscopic state is characterised by 29 scalar fields which correspond to the moments of the distribution function: mass density, hydrodynamic velocity, pressure tensor, absolute temperature, translational and rotational heat fluxes, hydrodynamic angular velocity and angular velocity flux. The balance equations for the 29 scalar fields are obtained from a transfer equation derived from the Enskog equation where the kinetic and potential parts of the new moments of the distribution function and production terms are calculated from Grad's distribution function for the basic fields. The transition from the 29 field theory to an eight field theory—with mass density, hydrodynamic velocity, absolute temperature and hydrodynamic angular velocity—leads to the determination of the transport coefficients of the Navier–Stokes and Fourier laws. The transport coefficients are functions of the normal and tangential restitution coefficients and of the local equilibrium radial distribution function. The transport coefficients in the limiting case of elastic rough spheres is also determined. [ABSTRACT FROM AUTHOR]

Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. [ABSTRACT FROM AUTHOR]

The second post-Newtonian hydrodynamic equations are analyzed within the framework of a plane wave solution. The hydrodynamic equations for the mass and momentum density are coupled with six Poisson equations for the Newtonian and post-Newtonian gravitational potentials. Perturbations of the basic fields and gravitational potentials from a background state by assuming plane wave representations lead to a dispersion relation where the Jeans instability condition emerges. The influence of the first and second post-Newtonian approximations on the Jeans mass is determined. It was shown that the relative difference of the first post-Newtonian and the Newtonian Jeans masses is negative while the one of the second post-Newtonian approximation is positive. The two contributions imply a smaller mass needed for an overdensity to initiate the gravitational collapse than the one given by the Newtonian theory. [ABSTRACT FROM AUTHOR]

Jeans instability is analyzed in an expanding universe within the framework of BGK model of the Boltzmann equation and Poisson equations. The background is characterized by a comoving Maxwellian distribution function and a spacetime Newtonian gravitational potential which satisfy the BGK model of the Boltzmann–Poisson equations without the necessity to invoke "Jeans swindle." The perturbations of the distribution function and Newtonian gravitational potentials from their background states are represented by plane waves of small amplitudes and a differential equation for the density contrast is determined. The density contrast differential equation was solved numerically and it is shown: (i) Jeans instability is characterized by perturbation wavelengths larger than Jeans wavelength where the density contrast grows with time. The growth of the density contrast is less accentuated for the case where the particle collisions are considered due to an energy dissipation; (ii) for perturbation wavelengths smaller than Jeans wavelength the density contrast has an oscillatory behavior in time and the oscillations for the case where the collisions are taken into account fade away in time due to the energy dissipation. [ABSTRACT FROM AUTHOR]

We present a model of an early universe where the sources of gravitational effects are a scalar field, a relativistic fluid based on Schutz's model and a self-interacting fermionic field. From the classical analysis based on the Hamiltonian formalism we show that the scale factor of the universe can be expressed in terms of a conformal time that emerges from the fluid's degrees of freedom. From the Wheeler–DeWitt equation, a wave packet solution as function of the conformal time is determined. It is shown that the combination of the scalar and the fermionic field furnishes a consistent quantum regime and a smooth transition to the classical description, working with the aid of the Bohmian mechanics and in particular with the concept of quantum potential. The influence of the presence of the scalar field is also discussed. [ABSTRACT FROM AUTHOR]

A cosmological model for the early universe is investigated where a Schutz uid and a fermionic field coupled to a gauge field are the sources of the gravitational field. The determination of the scale factor in the classical analysis follows from the Hamiltonian formulation together with Dirac's method for constrained systems. The expectation value of the scale factor in the quantum analysis is determined from the Wheeler{DeWitt equation. The singularity in the classical solution for the scale factor is avoided in the quantum solution where a bouncing from a minimum value of the scale factor is present. It is shown that: (i) the minimum value of the scale factor depends on the ratio of the fermionic coupling constant and the mass of the vectorial field; (ii) the classical and quantum solutions coincide for large values of the conformal time due to a dilution of the quantum effects with the time evolution; (iii) the behavior of the wave function probability density confirms that the maximum probability occurs when the scale factor has its minimum value equal to its expectation value; (iv) the quantum potential in the Bohmian formulation goes to infinity when the scale factor tends to zero avoiding the singularity at this point. [ABSTRACT FROM AUTHOR]

In this work we consider the scale-covariant formalism proposed by Canuto et al., 1 , 2 in order to map different eras of the universe. This technique considers a scale gauge function that can be adjusted by using different arguments like Dirac's large numbers hypothesis or a restriction on the particle production rate. A Chaplygin constituent shows to be a consistent idea to establish a mapping between an old decelerated–accelerated universe ruled by Einstein equations and an early universe, where a new equation of state appears together with a modified general relativity theory and a de Sitter universe then emerges. These properties are a direct consequence of the use of the scale-covariant formalism. Besides, a new discussion and remarks are presented related to the well-known barotropic constituent case. [ABSTRACT FROM AUTHOR]

The effects caused by the chemical reactions on the transport coefficients of a mixture of ideal gases which undergo a simple reversible symmetric reaction of the type A +A ... B + B are analyzed within the framework of a kinetic theory based on the Boltzmann equation. The analyzed system is closed to the final stage of a chemical reaction where the affinity is considered to be a small quantity and the system tends to the chemical equilibrium. This kind of reaction is known as "fast" reactions, because the reactive processes are of the same order as the elastic ones. The internal degrees of freedom of the molecules of the gas are not taken into account. This enables to represent the gas molecules as rigid spheres and therefore to determine the coefficients of thermal conductivity, diffusion, thermal-diffusion ratio, shear viscosity, and the forward reaction rate analytically. It was verified that some factors—among others, the concentration of the reagents (or products of the reaction), the activation energy, the heat of reaction, and the steric factor—can affect in a significant way the transport coefficients in reactive gas mixtures. [ABSTRACT FROM AUTHOR]

A model for an anisotropic pre-inflationary universe described by the Bianchi type-I metric is developed. A relativistic fluid of the Schutz formalism and a self-interacting fermionic field are considered as sources of the gravitational field. The classical analysis is based on the Hamiltonian formalism written in terms of the Misner variables and it is shown that the fluid degrees of freedom can be embodied by a conformal time variable. The three classical scale factors are obtained as functions of the conformal time. The quantum analysis follows from the de Broglie–Bohm formalism applied to the wave function which is a solution of the Wheeler–DeWitt equation and the three scale factors are also determined as functions of the conformal time. While the classical expressions for the scale factors show a singularity when the conformal time vanishes, their quantum expressions exhibit bouncing behavior. It is possible to adjust the behavior of the classical and quantum scale factors as functions of the conformal time so that they have a common isotropic behavior at late times with a dilution of the quantum effects. [ABSTRACT FROM AUTHOR]

In this work, a model for the pre-inflationary universe is developed where the sources of the gravitational field are a relativistic fluid and a self-interacting fermionic field. The inclusion of the relativistic fluid is based on Schutz's model. From the classical analysis based on the Hamiltonian formalism, it is shown that the fluid degrees of freedom can be embodied by a conformal time variable and an expression for the scale factor as function of the conformal time is obtained. From the Wheeler-DeWitt equation, the expected value for the scale factor as function of the conformal time is determined. It is shown that contrary to the classical solution, the expected value of the scale factor does not have a singularity, since it is preceded by a contracted phase up to a minimum value from which the universe begins to expand. Furthermore, from the plots of the classical and quantum solutions for the scale factor as functions of the conformal time it is shown that a decoherence of the quantum solution occurs for late times and both solutions coincide. [ABSTRACT FROM AUTHOR]

A cosmological model with a fermionic field and a massive bosonic field within the framework of the Einstein-Cartan theory is developed. The spacetime curvature is due to the matter-energy of the gravitational sources, whereas the torsion of the spacetime manifold follows from the spin density. From the numerical simulations it is shown that the fermionic spin density and the bosonic constituent answer for the transition from a decelerated to an accelerated era. The massive bosonic field behaves as dark energy, as it promotes the final accelerated period. During the initial decelerated era both constituents contribute, and the transition occurs as the torsion effect decreases with time. The exchange of energy between the constituents occurs via the gravitational field. [ABSTRACT FROM AUTHOR]

We analyze the properties of a generic cosmological fluid described by the van der Waals equation-of-state. Exact solutions for the energy-density evolution are found as implicit functions of the scale factor for a flat Friedmann-Robertson-Walker (FRW) spacetime. The possible values of the free parameter in the van der Waals equation are selected a posteriori, in accordance with asymptotic behaviors that are physically relevant. The stability of the model against small perturbations is studied through the hydrodynamic perturbations of the fluid for the relevant cases. It is found that a van der Waals fluid seems appropriate to describe noneternal inflationary scenarios. [ABSTRACT FROM AUTHOR]

A model for the universe with tachyonic and fermionic fields interacting through a Yukawa-type potential is investigated. It is shown that the tachyonic field answers for the initial accelerated regime and for the subsequent decelerated regime so that it behaves as an inflaton at early times and as a matter field at intermediate times, while the fermionic field has the role of a dark energy constituent, since it leads to an accelerated regime at later times. The interaction between the fields via a Yukawa-type potential controls the duration of the decelerated era, since a stronger coupling makes a shorter decelerated period. [ABSTRACT FROM AUTHOR]

In this work, the dynamics of self-gravitating systems composed by dark and baryonic matter is analyzed. Searching for a description of this dynamics, a system of collisionless Boltzmann equations for the two constituents and the Poisson equation for the gravitational field are employed. Through the solution of these equations, the collapse criterion is determined from a dispersion relation. The collapse occurs in an unstable region where the solutions grow exponentially with time. It is shown that the unstable region becomes larger if the dispersion velocity of dark matter becomes larger than the one of the baryonic matter. The results obtained are also compared with the case where only the dark matter is present. The model of the present work has a higher limit of instability and therefore exhibited an advantage in the structure formation. [ABSTRACT FROM AUTHOR]

Shear viscosity coefficient is calculated for both equilibrium and strongly non-equilibrium state-to-state vibrational distributions taking into account increasing diameters of vibrationally excited molecules. Under conditions of local thermal equilibrium, the effect of vibrational excitation on the shear viscosity coefficient is found to be negligible for temperatures below 5000 K. For T > 10 000 K, the contribution of excited states becomes important. Under non-equilibrium conditions characteristic for shock heated and supersonic expanding flows vibrational level populations deviate strongly from the Boltzmann distribution. Nevertheless, estimated coupled effect of molecular size and non-Boltzmann distributions on the shear viscosity coefficient is negligible. [ABSTRACT FROM AUTHOR]