Here's the breakdown:
* "Greek god" should be capitalized because it refers to a specific group of deities from Greek mythology.
* "theory" should not be capitalized unless it's the beginning of a sentence.
Therefore, the correct capitalization is "Greek God Theory" if it's at the beginning of a sentence, or "Greek god theory" if it's within a sentence.
However, it's important to note that the term "Greek god theory" isn't a widely recognized or established term.
* If you're talking about a specific theory related to Greek gods, you should use a more specific name, such as "The Theory of Olympian Power" or "The Origin of Greek Mythology Theory."
* If you're talking about the general study of Greek mythology, then "Greek mythology" is the correct term, and "Greek gods" would be used to refer to the deities.
It's always best to be clear and specific in your writing to avoid confusion.