Is the ontological argument for the existence of God a branch of theology?

I just found out that cosmology is a branch of theology, is ontology the same thing? What exactly is the ontological argument in laymen terms? Would the cosmological argument and ontological argument be good subjects to compare and contrast in a research paper? I’m looking for a good topic and haven’t really been able to wrap my head around this subject. Your Help is really appreciated

It is a popular subject in theology… I don’t know about "branch." The "greatest conceivable being" or the "necessary being" can be quite different from the "umoved mover" in a theological context… The cosmological proof my by more popular for like Deists. The proving of God and the nature/predicates of God are different subjects. Different "branches" of Theology disagree on the nature of God more than the proofs. (Atleast that’s my understanding… I’m a philosopher not a theologian.)

It would be a great paper subject… I wrote similar paper in first year. (It would be too broad for a graduate thesis.) I’ve explained both proofs in Y! answers before, but for you I’m going to refer you to the sources….

Stanford Page on Ontological

http://plato.stanford.edu/entries/ontological-arguments/

Stanford Page on Cosmological

http://plato.stanford.edu/entries/cosmological-argument/

Here are some really important references you will want to check out:
Summa Theologica (I,q.2,a.3) by Saint Thomas Aquinas
Proslogion by Anselm
Critique of Pure Reason by Immanual Kant
Meditiations (III) by Descartes
Physics (VIII, 4–6) by Aristotle
Metaphysics (XII, 1–6) by Aristotle

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EDIT – I see that you got "cosmology is a branch of theology" from an answer to your previous question. Although his answer was kindof correct in the definitions, that is a very misleading statement. I’ll answer that question too, try and clear up the confusion over the terms.