Darboux Cosmological Fluids in Comoving Time

Monthly Notices of the Royal Astronomical Society, 1998

A set of cosmological variables, which we shall refer to as "supercomoving variables," are presented which are an alternative to the standard comoving variables, particularly useful for describing the gas dynamics of cosmic structure formation. For ideal gas with a ratio of specific heats γ = 5/3, the supercomoving position, velocity, and thermodynamic properties (i.e. density, temperature, and pressure) of matter are constant in time in a uniform, isotropic, adiabatically expanding universe. Expressed in terms of these supercomoving variables, the nonrelativistic, cosmological fluid conservation equations of the Newtonian approximation and the Poisson equation closely resemble their noncosmological counterparts. This makes it possible to generalize noncosmological results and techniques to address problems involving departures from uniform, adiabatic Hubble expansion in a straightforward way, for a wide range of cosmological models. These variables were initially introduced by Shandarin (1980) to describe structure formation in matter-dominated models. In this paper, we generalize supercomoving variables to models with a uniform contribution to the energy density corresponding to a nonzero cosmological constant, domain walls, cosmic strings, a nonclumping form of nonrelativistic matter (e.g. massive neutrinos in the presence of primordial density fluctuations of small wavelength), or a radiation background. Each model is characterized by the value of the density parameter Ω 0 of the non-relativistic matter component in which density fluctuation is possible, and the density parameter Ω X0 of the additional, nonclumping component. For each type of nonclumping background, we identify families within which different values of Ω 0 and Ω X0 lead to fluid equations and solutions in supercomoving variables which are independent of the cosmological parameters Ω 0 and Ω X0 . We also generalize the description to include the effects of nonadiabatic processes such as heating, radiative cooling, thermal conduction and viscosity, as well as magnetic fields in the MHD approximation.

International Journal of Geometric Methods in Modern Physics, 2018

This paper is an attempt to revisit the Friedmann–Robertson–Walker (FRW) cosmological models under the new scenario of observational cosmology, which has established that the current universe is expanding with an increasing rate, in contrast to the earlier belief that the rate of expansion is constant or slowing down. This paper represents a model which encompasses both, earlier decelerating and the current accelerating universe, passing through a transition phase. The universe is assumed to be filled with two fluids, barotropic and dark energy. We have considered two cases; first, when these fluids are assumed to be non-interacting and second, when they interact with each other. Some physical, kinematic and geometric properties of the model are also discussed along with the acceptability and stability of the solution. The results found are very compatible with the established results as well as recent observations.

Environmental Science and Engineering, 2014

We review the role of fluids in cosmology by first introducing them in General Relativity and then by applying them to a FRW Universe's model. We describe how relativistic and non-relativistic components evolve in the background dynamics. We also introduce scalar fields to show that they are able to yield an inflationary dynamics at very early times (inflation) and late times (quintessence). Then, we proceed to study the thermodynamical properties of the fluids and, lastly, its perturbed kinematics. We make emphasis in the constrictions of parameters by recent cosmological probes.

Modern Physics Letters A

We analyze characteristic properties of two different cosmological models: (i) a one-component dark energy model where the bulk viscosity [Formula: see text] is associated with the fluid as a whole, and (ii) a two-component model where [Formula: see text] is associated with a dark matter component [Formula: see text] only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation-of-state [Formula: see text] with [Formula: see text] a constant. In the one-component model, we consider two possibilities, either to take [Formula: see text] proportional to the scalar expansion (equivalent to the Hubble parameter), in which case the evolution becomes critically dependent on the value of the small constant [Formula: see text] and the magnitude of [Formula: see text], or we consider the case [Formula: see text], where a de Sitter final stage is reached in the future. In the two-component model, we consider only the case where the da...

International Journal of Modern Physics D

From a hydrodynamicist’s point of view the inclusion of viscosity concepts in the macroscopic theory of the cosmic fluid would appear most natural, as an ideal fluid is after all an abstraction (exluding special cases such as superconductivity). Making use of modern observational results for the Hubble parameter plus standard Friedmann formalism, we may extrapolate the description of the universe back in time up to the inflationary era, or we may go to the opposite extreme and analyze the probable ultimate fate of the universe. In this review, we discuss a variety of topics in cosmology when it is enlarged in order to contain a bulk viscosity. Various forms of this viscosity, when expressed in terms of the fluid density or the Hubble parameter, are discussed. Furthermore, we consider homogeneous as well as inhomogeneous equations of state. We investigate viscous cosmology in the early universe, examining the viscosity effects on the various inflationary observables. Additionally, we...

Journal of Cosmology and Astroparticle Physics, 2010

We study Friedmann-Robertson-Walker cosmological models with matter content composed of two perfect fluids $\rho_1$ and $\rho_2$, with barotropic pressure densities $p_1/ \rho_1=\omega_1=const$ and $p_2/ \rho_2=\omega_2=const$, where one of the energy densities is given by $\rho_1=C_1 a^\alpha + C_2 a^\beta$, with $C_1$, $C_2$, $\alpha$ and $\beta$ taking constant values. We solve the field equations by using the conservation equation without breaking

Arxiv preprint astro-ph/9605176, 1996

Physics Letters A, 2015

For non-zero cosmological constant Λ, we show that the barotropic FRW cosmologies as worked out in the comoving time lead in the radiation-dominated case to scale factors of identical form as for the Chiellini dissipative scale factors in conformal time obtained recently by us in Phys. Lett. A 379 (2015) 882-887. This is due to the Ermakov equation which is obtained in this case. For zero cosmological constant, several textbook solutions are provided as particular cases of Λ = 0.

Classical and Quantum Gravity, 2003

We consider the homogeneous and isotropic cosmological fluid dynamics which is compatible with a homothetic, timelike motion, equivalent to an equation of state ρ + 3P = 0. By splitting the total pressure P into the sum of an equilibrium part p and a non-equilibrium part Π, we find that on thermodynamical grounds this split is necessarily given by p = ρ and Π = − 4 3 ρ, corresponding to a dissipative stiff (Zel'dovich) fluid.

arXiv: General Relativity and Quantum Cosmology, 1998

The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations for a cosmological fluid, the present lectures cover some of the same ground as a previous set of Carg\`{e}se lectures \cite{ell73}, but they then go on to give (ii) the full set of corresponding tetrad equations, (iii) a classification of cosmological models with exact symmetries, (iv) a brief discussion of some of the most useful exact models and their observational properties, and (v) an introduction to the gauge-invariant and 1+3 covariant perturbation theory of almost-Friedmann-Lema\^{\i}tre-Robertson-Walker universes, with a fluid description for the matter and a kinetic theory description of the radiation.