Dictionary: met·a·phys·ics
n.
1. (used with a sing. verb) Philosophy. The branch of philosophy that examines the nature of reality, including the relationship between mind and matter, substance and attribute, fact and value.
2. (used with a pl. verb) The theoretical or first principles of a particular discipline: the metaphysics of law.
3. (used with a sing. verb) A priori speculation upon questions that are unanswerable to scientific observation, analysis, or experiment.
4. (used with a sing. verb) Excessively subtle or recondite reasoning.
[From pl. of Middle English methaphisik, from Medieval Latin metaphysica, from Medieval Greek (ta) metaphusika, from Greek (Ta) meta (ta) phusika, (the works) after the Physics, the title of Aristotle's treatise on first principles (so called because it followed his work on physics) : meta, after; see meta- + phusika, physics; see physics.]
Dictionary: cos·mol·o·gy
n., pl., -gies.
1. The study of the physical universe considered as a totality of phenomena in time and space.
2.
1. The astrophysical study of the history, structure, and constituent dynamics of the universe.
2. A specific theory or model of this structure and these dynamics.
Yes, these would both apply to the former position of man searching for his place in the universe, as they do not presume the existence of a supernatural force. Metaphysics as a branch of philosophy and cosmology as a branch of science. The latter position which does presume such a presence might be considered, as an (arguably) academic study, theology which would include such topics as spiritualism, superstition and transcendence.