Big History refers to the historical studies starting from the beginning of time, throughout the eons and to the present day. It is very interesting and important to ponder and study as it gives the perspective of long human trends and ideas (macro-history) and how these fit within larger time frames themselves (deep history).
There's no rule against big history per se. However, many 'big history' questions do fall afoul of our 'example seeking' rule, which covers both explicit requests for examples ('tell me examples of famous chefs in history') as well as implicit requests for examples ('what were restaurants like throughout history'). That is, if a question covers such broad scope and variety that a single, in-depth and comprehensive answer isn't really possible (and would instead inspire a series of partial answers from different perspectives), it runs afoul of this rule, and we'd encourage the asker to narrow the scope of the question more precisely. This isn't necessarily because such questions or invalid or uninteresting, but because our rules serve to encourage the best possible chance for a good answer rather than define the full scope of historical inquiry. Either way, this rule cuts out plenty of big history, perhaps hinting at the reality that a lot of 'big history' is trying to answer questions that are simply too broad and complex to be addressed effectively in a single book, let alone a Reddit post.
I don't want to pretend that this is the entire genre, of course. Particularly for fields like environmental history, a longer time frame often makes a lot of analytic sense, and good questions using longer time frames do get asked here. We also always welcome people to ask about specific texts or the historiography surrounding a particular subject or approach. But most of the 'big history' that gets asked about here is more of the 'popular book I picked up at an airport' variety. We have an entire section of our FAQ dedicated to slightly annoyed historians writing about Jared Diamond's Guns, Germs and Steel, for instance. Questions asking about the field more (rather, less) broadly would be very welcome!
I can't see anything in the sub's rules against it, as long as you're still asking a specific question.
The one potential sticking point in there is the rule against discussion of events from within the last 20 years.
While research published in the last 20 years is fine, discussion of events within the last 20 years isn't.
So, any trends and patterns that hold true for the recent past should be discussed without particularly commenting on any 21^st Century examples.