Implications of singularity theorem for non-singular universe

The singularity theorem by Penrose shows that a spacetime singularity arises in certain universal situations. The existence of a spacetime singularity is thought to represent a breakdown in the validity of theories such as general relativity and the phenomenological models of the universe. Thus, if we could build a correct model that describes the beginning of the universe, the universe predicted by that model should be non-singular. In this talk, we will discuss general properties that a non-singular universe must satisfy in order to avoid the singularity theorem. In particular, we will see that the universe must be, in some sense, smaller than the corresponding closed de Sitter spacetime.