  We study the phase transition from quark-gluon plasma to hadrons in the early
universe in the context of non-equilibrium thermodynamics. According to the
standard model of cosmology, a phase transition associated with chiral symmetry
breaking after the electro-weak transition has occurred when the universe was
about $1-10\mu s$ old. We focus attention on such a phase transition in the
presence of a viscous relativistic cosmological background fluid in the
framework of non-detailed balance Ho\v{r}ava-Lifshitz cosmology within an
effective model of QCD. We consider a flat Friedmann-Robertson-Walker Universe
filled with a non-causal and causal bulk viscous cosmological fluid
respectively and investigate the effects of the running coupling constants of
Ho\v{r}ava-Lifshitz gravity, $\lambda$, on the evolution of the physical
quantities relevant to a description of the early universe, namely, the
temperature $T$, scale factor $a$, deceleration parameter $q$ and dimensionless
ratio of the bulk viscosity coefficient to entropy density $\frac{\xi}{s}$. We
assume that the bulk viscosity cosmological background fluid obeys the
evolution equation of the steady truncated (Eckart) and full version of the
Israel-Stewart fluid, respectively.
