  We consider the evolution of a flat, isotropic and homogeneous
Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous
cosmological fluid, that can be characterized by an ultra-relativistic equation
of state and bulk viscosity coefficient obtained from recent lattice QCD
calculations. The basic equation for the Hubble parameter is derived under the
assumption that the total energy in the Universe is conserved. By assuming a
power law dependence of bulk viscosity coefficient, temperature and relaxation
time on energy density, an approximate solution of the field equations has been
obtained, in which we utilized equations of state from recent lattice QCD
simulations QCD and heavy-ion collisions to derive an evolution equation. In
this treatment for the viscous cosmology, we found no evidence for singularity.
For example, both Hubble parameter and scale factor are finite at $t=0$, $t$ is
the comoving time. Furthermore, their time evolution essentially differs from
the one associated with non-viscous and ideal gas. Also thermodynamic
quantities, like temperature, energy density and bulk pressure remain finite as
well. In order to prove that the free parameter in our model does influence the
final results, qualitatively, we checked out other articular solutions.
