  We study the formation of marginally trapped surfaces in the head-on
collision of two shock waves in de Sitter space-time as a function of the
cosmological constant and the shock wave energy. We search for a marginally
trapped surface on the past light cone of the collision plane.
  For space-time dimension $D\geq3$ there exists a critical value of the shock
wave energy above which there is no trapped surface of this type. For $D>3$ the
critical value of the shock wave energy depends on the de Sitter radius, and
there is no this type trapped surface formation for a large cosmological
constant. For D=3, the critical value of the shock wave energy is independent
of the cosmological constant. At the critical point the trapped surface is
finite. Below the critical energy value, the area of trapped surface depends on
the cosmological constant and the shock wave energy.
