A phase space analysis for nonlinear bulk viscous cosmology

2016

By means of a combined use of the type Ia supernovae and H(z) data tests, together with the study of the asymptotic properties in the equivalent phase space -through the use of the dynamical systems tools -we demonstrate that the bulk viscous matter-dominated scenario is not a good model to explain the accepted cosmological paradigm, at least, under the parametrization of bulk viscosity considered in this paper. The main objection against such scenarios is the absence of conventional radiation and matter-dominated critical points in the phase space of the model. This entails that radiation and matter dominance are not generic solutions of the cosmological equations, so that these stages can be implemented only by means of unique and very specific initial conditions, i. e., of very unstable particular solutions. Such a behavior is in marked contradiction with the accepted cosmological paradigm which requires of an earlier stage dominated by relativistic species, followed by a period of conventional non-relativistic matter domination, during which the cosmic structure we see was formed. Also, we found that the bulk viscosity is positive just until very late times in the cosmic evolution, around z < 1. For earlier epochs it is negative, been in tension with the local second law of thermodynamics.

Journal of Cosmology and Astroparticle Physics, 2013

By means of a combined use of the type Ia supernovae and H(z) data tests, together with the study of the asymptotic properties in the equivalent phase space -through the use of the dynamical systems tools -we demonstrate that the bulk viscous matterdominated scenario is not a good model to explain the accepted cosmological paradigm, at least, under the parametrization of bulk viscosity considered in this paper. The main objection against such scenarios is the absence of conventional radiation and matter-dominated critical points in the phase space of the model. This entails that radiation and matter dominance are not generic solutions of the cosmological equations, so that these stages can be implemented only by means of unique and very specific initial conditions, i. e., of very unstable particular solutions. Such a behavior is in marked contradiction with the accepted cosmological paradigm which requires of an earlier stage dominated by relativistic species, followed by a period of conventional non-relativistic matter domination, during which the cosmic structure we see was formed. Also, we found that the bulk viscosity is positive just until very late times in the cosmic evolution, around z < 1. For earlier epochs it is negative, been in tension with the local second law of thermodynamics.

Classical and Quantum Gravity

We probe into universes filled with Quark Gluon Plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the Quark Gluon Plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor R(t) which goes to zero only asymptotically. The cosmological model with bulk viscosity is extended to include a Cosmological Constant. The previous results are contrasted with the cosmology with non-zero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann-Lamaître-Robertson-Walker metric. To this end we use a version of the energy-momentum tensor from the Müller-Israel-Stewart theory which leads to causal Navier-Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges to be non-singular.

arXiv (Cornell University), 2015

We discuss the possibility to implement a viscous cosmological model, attributing to the dark matter component a behaviour described by bulk viscosity. Since bulk viscosity implies negative pressure, this rises the possibility to unify the dark sector. At the same time, the presence of dissipative effects may alleviate the so called small scale problems in the ΛCDM model. While the unified viscous description for the dark sector does not lead to consistent results, the non-linear behaviour indeed improves the situation with respect to the standard cosmological model.

Physical Review D

We investigate the out-of-equilibrium dynamics of viscous fluids in a spatially flat Friedmann-Lemaître-Robertson-Walker cosmology using the most general causal and stable viscous energymomentum tensor defined at first order in spacetime derivatives. In this new framework a pressureless viscous fluid having equilibrium energy density ρ can evolve to an asymptotic future solution in which the Hubble parameter approaches a constant while ρ → 0, even in the absence of a cosmological constant (i.e., Λ = 0). Thus, while viscous effects in this model drive an accelerated expansion of the universe, the equilibrium energy density itself vanishes, leaving behind only the acceleration. This behavior emerges as a consequence of causality in first-order theories of relativistic fluid dynamics and it is fully consistent with Einstein's equations.

We consider the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble parameter, generalizing the evolution equation in the case of constant gravitational coupling and cosmological term is derived, under the supplementary assumption that the total energy of the Universe is conserved. By assuming that the cosmological constant is proportional to the square of the Hubble parameter and a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density of the cosmological fluid, two classes of exact solutions of the field equations are obtained. In the first class of solutions the Universe ends in an inflationary era, while in the second class of solutions the expansion of the Universe is noninflationary for all times. In both models the cosmological "constant" is a decreasing function of time, while the gravitational "constant" increases in the early period of evolution of the Universe, tending in the large time limit to a constant value.

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...

Astrophysics and Space Science, 1994

Singularity-free Robertson-Walker cosmological models (RWCM) are developed by considering the cosmic matter as composed of interacting viscous fluid (with zero bulk viscosity) and massive scalar (meson) field. Solutions are obtained for two different cases, viz., when the Hubble's parameter H is epoch independent and when H is epoch dependent. A solution corresponding to RWCM with only the massive scalar field as the matter content is also presented. Essential physical behaviour of the models developed are discussed in detail.

Physics Letters B, 2006

The statefinder diagnostic pair is adopted to differentiate viscous cosmology models and it is found that the trajectories of these viscous cosmology models on the statefinder pair s − r plane are quite different from those of the corresponding non-viscous cases. Particularly for the quiessence model, the singular properties of state parameter w = −1 are obviously demonstrated on the statefinder diagnostic pair planes. We then discuss the entropy of the viscous / dissipative cosmology system which may be more practical to describe the present cosmic observations as the perfect fluid is just a global approximation to the complicated cosmic media in current universe evolution. When the bulk viscosity takes the form of ζ = ζ1ȧ/a(ζ1 is constant), the relationship between the entropy S and the redshift z is explicitly given out. We find that the entropy of the viscous cosmology is always increasing and consistent with the thermodynamics arrow of time for the universe evolution. With the parameter constraints from fitting to the 157 gold data of supernova observations, it is demonstrated that this viscous cosmology model is rather well consistent to the observational data at the lower redshifts, and together with the diagnostic statefinder pair analysis it is concluded that the viscous cosmic models tend to the favored ΛCDM model in the later cosmic evolution, agreeable to lots of cosmological simulation results, especially to the fact of confidently observed current accelerating cosmic expansion.

Arxiv preprint gr-qc/0508038, 2005

We discuss a modified form of gravity implying that the action contains a power α of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for a general α. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2α − 1) of the scalar expansion. In Einstein's gravity, where α = 1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the authors, there exists in principle a viscosity-driven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.