In this chapter we will see it is possible to generalize the topological censorship to the cosmological case. This work was done in collaboration with K.Schleich and J. Erickson. In the proof of the lemma 2 of the topological censorship we use the hypotheses that the spacetime is asymptotically flat . What we tried is to relax this condition. If we don't assumed the asymptotic flatness but rather a more general definition of asymptotically nice behavior, then we can apply that theorem to spacetime like de Sitter . This is especially interesting in cosmology in the context of inflation .