  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.
