In this paper, an alternative approach to cosmology is discussed. Rather than starting from the field equations of general relativity, one can investigate the probability space of all possible universes and try to decide what kind of universe is the most probable one. Here two quite different models for this probability space are presented: the combinatorial model and the random curvature model. In addition, it is briefly discussed how these models could be applied to explain two fundamental problems of cosmology: Time’s Arrow and the accelerating expansion.