A DGP brane-world model with a perfect fluid brane matter including a Brans-Dicke (BD) scalar field on brane has been utilized to investigate the problem of the quark-hadron phase (QHP) transition in early times of the Universe evolution. The presence of the BD scalar field comes up with some modification terms in the Friedmann equation. Since the behavior of phase transition strongly depends on the basic evolution equations, even a small change in these relations might come to interesting results about the time of transition. The phase transition is investigated using two scenarios of the first-order phase transition and smooth crossover phase transition. For first-order scenario, which is used for intermediate temperature regime, the evolution of the physical quantities, such as temperature and scale factor, are investigated before, during and after the phase transition. The results show that the transition occurs in about micro-second. In the next part, the phenomenon is studied by assuming a smooth crossover transition where the lattice QCD data is utilized to obtain a realistic equation of state for the matter. The investigation for this part is performed in two regimes of high and low-temperature. Using trace anomaly in the high-temperature regime specifies a simple equation of state which states that the quark-gluon behaves like radiation. However, in the low-temperature regime, the trace anomaly is affected by discretization effects, and the hadron resonance gas model is utilized instead. Using this model, a more realistic equation of state could be found in the low-temperature regime. The crossover phase transition in both regimes is considered. The results determine that the transition occurs at the time around a few micro-second. Also, it is realized that the transition in the low-temperature regime occurs after the transition in the high-temperature regime.
