Horava-Lifshitz early universe phase transition beyond detailed balance

The early universe is believed to have undergone a QCD phase transition to hadrons at about $10\mu s$ after the big bang. We study such a transition in the context of the non-detailed balance Horava-Lifshitz theory by investigating the effects of the dynamical coupling constant $\lambda$ in a flat universe. The evolution of the relevant physical quantities, namely the energy density $\rho$, temperature $T$, scale factor $a$ and the Hubble parameter $H$ is investigated before, during and after the phase transition, assumed to be of first order. Also, in view of the recent lattice QCD simulations data, we study a cross-over phase transition of the early universe whose results are based on two different sets of lattice data.