Cosmology is the study of the physical universe considered as a totality of phenomena in time and space. In Philosophy it even relates to causality and freedom.

It is not possible to interpret the texts of Plato - including those dealing with Politics - without understanding his Cosmology. For the cosmology of Plato is different from the cosmologies of classical theologies (the Christian Theology for example), it would be a great non-sense to discuss Religion in Plato's Republic with Classical Theology in mind.

Plato's Cosmology is essentially gnostic (like those of one of his mentor Pythagorus) i.e. like most ancient Greeks, he believed (see the end if he really believes) in many "gods" as Demiurge-gods (a demiurge is a worker so these gods were just workers for Nature). One Demiurge-god created the Cosmos - including man - but he didn't create it "out of nothing", but rather out of some pre-existing immaterial Forms (the "stuff" needed was already there).

So for Plato there is a "transcendental" realm of immaterial Forms and that realm is, according to him, the only true reality, the only things that are "really real", that are really Being. Material things would be only appearances of the Forms, like dreams, only "copies" or "images" of the "really real" Forms. Plato's ultimate "god" or "the One" does not belong to this transcendent realm of Being or Forms, but rather, in Plato's words, "lies beyond it".

Finally, Plato repeats that these theories are to be considered as "likely myths" not as definite truths. Unfortunately those who rever Plato doesn't seem to take it into account and embrace Plato litteraly. In fact it is even said that Plato admitted in Parmenides that his Theory of Forms was wrong and wouldn't work.