Thermodynamics of viscous matter and radiation in the early universe (original) (raw)
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Thermodynamics in the viscous early universe
Canadian Journal of Physics, 2010
Assuming that the matter in the background geometry is a free gas and that no phase transitions were occurring in the early Universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, the scaling factor a, and the curvature parameter k, can be derived from this simple model, which on one hand fulfills and entirely obeys the laws of thermodynamics, and on the other hand, its results are compatible with the Friedmann–Robertson–Walker model and the Einstein field equations. Including a finite bulk viscosity coefficient leads to important changes in all these cosmological quantities. Accordingly, our picture about the evolution of the Universe and its astrophysical consequences seems to undergoing a radical revision. We find that k strongly depends on the thermodynamics of background matter. The time scale at which negative curvature might take place depends on the relation betw...
Viscous cosmology for early- and late-time universe
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...
Early viscous universe with variable gravitational and cosmological 'constants
Classical and Quantum Gravity 24 (2007) 455-474
Einstein's field equations with variable gravitational and cosmological 'constants' are considered in the presence of bulk viscosity for a spatially flat homogeneous and isotropic universe. Solutions are obtained by using a 'gamma-law' equation of state p = (γ - 1)ρ, where the adiabatic parameter γ varies continuously as the universe expands. A unified description of the early evolution of universe is presented with a number of possible assumptions on the bulk viscous term and gravitational constant in which an inflationary phase is followed by radiation-dominated phase. We investigate the cosmological model with constant and time-dependent bulk viscosity (proportional to power function of energy density and to Hubble parameter) along with constant and variable gravitational constant. The effect of viscosity is shown to affect the past and future of the universe. In all cases, the cosmological constant Λ is found to be positive and a decreasing function of time, which supports the results obtained from recent supernovae Ia observations. The possibility that the present acceleration of the universe is driven by a kind of viscous fluid is explained. At the background level this model is similar to the generalized Chaplygin gas model. The physical and geometrical significance of the early cosmological models has also been discussed.
Thermodynamic aspects of entropic cosmology with viscosity
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.
Dissipative Processes in the Early Universe: Bulk Viscosity
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.
General Relativity and Gravitation, 1989
A new type of cosmological history which includes large-scale entropy production is proposed. These cosmologies are based on a reinterpretation of the matter-energy stress tensor in Einstein's equations. This modifies the usual adiabatic energy conservation laws, thereby leading to a possible irreversible matter creation. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. This new point of view results from the consideration of thermodynamics of open systems in the framework of cosmology. It appears that the usual initial singularity is structurally unstable with respect to irreversible matter creation. The corresponding cosmological history therefore starts from an instability of the vacuum rather than from a singularity. The universe evolves through an inflationary phase. This appears to be an attractor independent of the initial vacuum fluctuation.
Entropy
Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel–Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel–Stewart, the differential equation...
Remarks on Cosmological Bulk Viscosity in Different Epochs
Symmetry
The intention of this paper is mainly two-fold. First, we point out a striking numerical agreement between the bulk viscosity in the lepton era calculated by Husdal (2016) and our own calculations of the present-day bulk viscosity when the functional form is ζ ∼ ρ . From a phenomenological point of view, we thus seem to have an ansatz for the viscosity, which bridges the infancy of the Universe (∼1 s) with the present. This can also be looked upon as a kind of symmetry between the early-time cosmology and the present-day cosmology: it is quite remarkable that the kinetic theory-based bulk viscosity in the early universe and the experimentally-based bulk viscosity in the present universe can be covered by the same simple analytical formula. Second, we consider the Kasner universe as a typical anisotropic model of Bianchi-Type I, investigating whether this geometrical model is compatible with constant viscosity coefficients in the fluid. Perhaps surprisingly, the existence of a shear ...
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.