[subject] + might/may/could + [verb]
[subject] + might not/may not + [verb]
Might, may and could say that something is possible now or in the future, but you aren't sure. All three are followed by the base verb (go, be, rain), and they don't change: there is no -s with he, she or it.
The meaning is almost the same. May sounds a little more formal. Might is the most common in speech.
The negative is might not or may not: perhaps something won't happen, or perhaps it isn't true.
Could not doesn't mean "perhaps not". When you talk about possibility, couldn't means it is impossible.
Maybe (one word) is an adverb meaning "perhaps". May be (two words) is the verb.
Add have + past participle to talk about what possibly happened.