Critical Formation of Trapped Surfaces in the Collision of Non-expanding Gravitational Shock Waves in de Sitter Space-Time

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.