I am newcommer on this site , and would like to know whether we can ask questions relating to cosmology on this site?. As I am a enthusiast in both subjects. But these are not my professions. It is quite possible that I might be asking a non related question. Also I would like to know that ,can we ask question's related to ancient astronomy and it's findings?.As they are not scientific questions, but will be relating to history of astronomy. So requesting calrification.
Yes, scientific cosmology is perfectly acceptable here, and ancient astronomy (note: not astrology) is generally regarded as on topic as well, though we don't have many with expertise in the topic of ancient astronomy, to my knowledge.
History of astronomy is also covered to some extent at History SE.
I'd like to point out that questions about the history of astronomy can also be asked on History of Science and Mathematics SE, hsm.stackexchange.com. They may fit better there since, as called2voyage points out, this site doesn't have many with expertise in the topic of ancient astronomy.