  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.
