Remarks on Cosmological Bulk Viscosity in Different Epochs

Monthly Notices of the Royal Astronomical Society, 1996

A universe consisting of two interacting perfect fluids with the same 4-velocity is considered. A heuristic mean free time argument is used to show that the system as a whole cannot also be perfect, but necessarily implies a non-vanishing bulk viscosity. A new formula for the bulk viscosity is derived and compared with corresponding results of radiative hydrogynamics.

Entropy

We derive a general formalism for bulk viscous solutions of the energy-conservation-equation for ρ(a, ζ), both for a single-component and a multicomponent fluid in the Friedmann universe. For our purposes these general solutions become valuable in estimating order of magnitude of the phenomenological viscosity in the cosmic fluid at present. H(z) observations are found to put an upper limit on the magnitude of the modulus of the present day bulk viscosity. It is found to be ζ 0 ∼ 10 6 Pa s , in agreement with previous works. We point out that this magnitude is acceptable from a hydrodynamic point of view. Finally, we bring new insight by using our estimates of ζ to analyse the fate of the future universe. Of special interest is the case ζ ∝ √ ρ for which the fluid, originally situated in the quintessence region, may slide through the phantom barrier and inevitably be driven into a big rip. Typical rip times are found to be a few hundred Gy.

Il Nuovo Cimento B, 1994

The e ect of bulk viscisity on the evolution of the homogeneous and isotropic cosmological models is considered. Solutions are found, with a barotropic equation of state, and a viscosity coef-cient that is proportional to a power of the energy density o f the universe. For at space, power law expansions, related to extended in ation are found as well as exponential solutions, related to old in ation; also a solution with expansion that is an exponential of an exponential of the time is found.

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...

International Journal of Modern Physics D, 2020

We describe the evolution of the early and late universe from thermodynamic considerations, using the generalized nonextensive Tsallis entropy with a variable exponent. A new element in our analysis is the inclusion of a bulk viscosity in the description of the cosmic fluid. Using the generalized Friedmann equation, a description of the early and the late universe is obtained.

Classical and Quantum Gravity, 1997

Multidimensional cosmological model describing the evolution of a fluid with shear and bulk viscosity in n Ricci-flat spaces is investigated. The barotropic equation of state for the density and the pressure in each space is assumed. The second equation of state is chosen in the form when the bulk and the shear viscosity coefficients are inversely proportional to the volume of the Universe. The integrability of Einstein equations reads as a colinearity constraint between vectors which are related to constant parameters in the first and second equations of state. We give exact solutions in a Kasner-like form. The processes of dynamical compactification and the entropy production are discussed. The non-singular D-dimensional isotropic viscous solution is singled out.

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.

Physical Review D, 1997

A Bianchi type-I metric of the Kasner form is used as input in Einstein's equations to explore which consequences thereby occur for the equation of state for the cosmic fluid. Both shear viscosity and bulk viscosity coefficients are assumed to be present. The solutions of Einstein's equations can naturally be categorized into two classes. Either the space becomes anisotropic, and the equation of state is determined once the Kasner parameters p i are given. Or the space becomes isotropic, and the equation of state emerges in the conventional form p/ϭ␥Ϫ1 with a definite value of ␥. We also calculate the rate of entropy production per particle, and find that becomes as large as of order 10 4 s Ϫ1 if we go back to the very early universe, t ϳ10 Ϫ4 s. We also discuss the possibility of testing the anisotropy of the universe by means of redshift experiments. ͓S0556-2821͑97͒06218-8͔

Arxiv preprint arXiv:0911.4105, 2009

In this talk, we discuss one of the dissipative processes which likely take place in the Early Universe. We assume that the matter filling the isotropic and homogeneous background is to be described by a relativistic viscous fluid characterized by an ultra-relativistic equation of state and finite bulk viscosity deduced from recent lattice QCD calculations and heavy-ion collisions experiments. We concentrate our treatment to bulk viscosity as one of the essential dissipative processes in the rapidly expanding Early Universe and deduce the dependence of the scale factor and Hubble parameter on the comoving time t. We find that both scale factor and Hubble parameter are finite at t = 0, revering to absence of singularity. We also find that their evolution apparently differs from the one resulting in when assuming that the background matter is an ideal and non-viscous fluid.

Physical Review D, 1996

The full causal Müller-Israel-Stewart (MIS) theory of dissipative processes in relativistic fluids is applied to a flat, homogeneous and isotropic universe with bulk viscosity. It is clarified in which sense the so called truncated version is a reasonable limiting case of the full theory. The possibility of bulk viscosity driven inflationary solutions of the full theory is discussed. As long as the particle number is conserved almost all these solutions exhibit an exponential increase of the temperature. Assuming that the bulk viscous pressure of the MIS theory may also be interpreted as an effective description for particle production processes, the thermodynamical behaviour of the Universe changes considerably. In the latter case the temperature increases at a lower rate or may remain constant during a hypothetical de Sitter stage, accompanied by a substantial growth of the comoving entropy.