Key words Transport properties of quark-gluon plasma, standard cosmological model, early universe, viscous equations of state.In the present work a study is given for the evolution of a flat, isotropic and homogeneous universe, which is filled with a causal bulk viscous cosmological fluid. We describe the viscous properties by an ultrarelativistic equation of state, and bulk viscosity coefficient obtained from recent lattice QCD calculations. The basic equation for the Hubble parameter is derived by using the energy equation obtained from the assumption of the covariant conservation of the energy-momentum tensor of the matter in the universe. By assuming a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density, we derive the evolution equation for the Hubble function. By using the equations of state from recent lattice QCD simulations and heavy-ion collisions we obtain an approximate solution of the field equations. In this treatment for the viscous cosmology, no evidence for singularity is observed. For example, both the Hubble parameter and the scale factor are finite at t = 0, where t is the comoving time. Furthermore, their time evolution essentially differs from the one associated with non-viscous and ideal gas. Also it is noticed that the thermodynamic quantities, like temperature, energy density and bulk pressure remain finite. Particular solutions are also considered in order to prove that the free parameter in this model does qualitatively influence the final results.

Key words Viscosity, quark deconfinement, thermal conduction in gases, quantum field theory.Assuming that the Hagedorn fluid composed of known particles and resonances with masses m < 2 GeV obeys the first-order theory (Eckart) of relativistic fluid, we discuss the transport properties of QCD confined phase. Based on the relativistic kinetic theory formulated under the relaxation time approximation, expressions for bulk and shear viscosity in thermal medium of hadron resonances are derived. The relaxation time in the Hagedorn dynamical fluid exclusively takes into account the decay and eventually van der Waals processes. We comment on the in-medium thermal effects on bulk and shear viscosity and averaged relaxation time with and without the excluded-volume approach. As an application of these results, we suggest the dynamics of heavy-ion collisions, non-equilibrium thermodynamics and the cosmological models, which require thermo-and hydro-dynamics equations of state.

We consider the influence of the perturbative bulk viscosity on the evolution of the Hubble parameter in the QCD era of the early Universe. For the geometry of the Universe we assume the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker metric, while the background matter is assumed to be characterized by barotropic equations of state, obtained from recent lattice QCD simulations, and heavy-ion collisions, respectively. Taking into account a perturbative form for the bulk viscosity coefficient, we obtain the evolution of the Hubble parameter, and we compare it with its evolution for an ideal (non-viscous) cosmological matter. A numerical solution for the viscous QCD plasma in the framework of the causal Israel-Stewart thermodynamics is also obtained. Both the perturbative approach and the numerical solution qualitatively agree in reproducing the viscous corrections to the Hubble parameter, which in the viscous case turns out to be slightly different as compared to the non-viscous case. Our results are strictly limited within a very narrow temperature-or time-interval in the QCD era, where the quark-gluon plasma is likely dominant.

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