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We study the phase transition from quark-gluon plasma to hadrons in the earlyuniverse in the context of non-equilibrium thermodynamics. According to thestandard model of cosmology, a phase transition associated with chiral symmetrybreaking after the electro-weak transition has occurred when the universe wasabout $1-10\mu s$ old. We focus attention on such a phase transition in thepresence of a viscous relativistic cosmological background fluid in theframework of non-detailed balance Ho\v{r}ava-Lifshitz cosmology within aneffective model of QCD. We consider a flat Friedmann-Robertson-Walker Universefilled with a non-causal and causal bulk viscous cosmological fluidrespectively and investigate the effects of the running coupling constants ofHo\v{r}ava-Lifshitz gravity, $\lambda$, on the evolution of the physicalquantities relevant to a description of the early universe, namely, thetemperature $T$, scale factor $a$, deceleration parameter $q$ and dimensionlessratio of the bulk viscosity coefficient to entropy density $\frac{\xi}{s}$. Weassume that the bulk viscosity cosmological background fluid obeys theevolution equation of the steady truncated (Eckart) and full version of theIsrael-Stewart fluid, respectively.

Cosmological QCD phase transition in steady non-equilibrium dissipative Ho\v{r}ava-Lifshitz early universe