The early universe is believed to have undergone a QCD phase transition to hadrons at about 10µs 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 λ in a flat universe. The evolution of the relevant physical quantities, namely the energy density ρ, 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.

Based on the assumptions of the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electroweak transition has occurred at approximately 10µ seconds after the Big Bang to convert a plasma of free quarks and gluons into hadrons. We consider such a phase transition in the context of a deformed Horava-Lifshitz cosmology. The Friedmann equation for the deformed Horava-Lifshitz universe is obtained using the entropic interpretation of gravity, proposed by Verlinde. We investigate the effects of the parameter ω appearing in the theory on the evolution of the physical quantities relevant to a description of the early universe, namely, the energy density and temperature before, during and after the phase transition. Finally, we study the cross-over phase transition in both high and low temperature regions in view of the recent lattice QCD simulations data.