  We consider the meson and baryon production in the quark-gluon plasma as
applied to the early Universe and ultrarelativistic heavy ion collisions in
collider. The essential feature of our investigation is to take into account a
potential barrier for quarks under meson and baryon production. We have used
the Boltzmann equation to describe kinetic processes of quark fusion. We have
derived analytic expressions for solutions of kinetic equations. This permits
to find the dependence of reaction rate on a time, temperature, mass and charge
of quarks as well as on a string tension connected with the confining
potential. Next we have considered in detail the meson and baryon production
for some concrete kinetic processes in collisions of ultrarelativistic heavy
ions. Exactly the same results will be as well true for processes in expanding
Universe
