Effect of extrinsic curvature on quark--hadron phase transition

The last phase transition predicted by the standard model of particle physics took place at the QCD scale $T\sim200$ MeV when the universe was about $t\sim10^{-5}$ seconds old and the Hubble radius was around 10 Km. In this paper, we consider the quark--hadron phase transition in the context of brane-world cosmology where our universe is a 3-brane embedded in a $m$-dimensional bulk and localization of matter on the brane is achieved by means of a confining potential. We study the behavior of the physical quantities relevant to the description of the early universe like the energy density, temperature and scale factor, before, during, and after the phase transition and investigate the effects of extrinsic curvature on the cosmological phase transition. We show that the brane-world effects reduce the effective temperature of the quark--gluon plasma and of the hadronic fluid. Finally, we discuss the case where the universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles.