If food is in my hand, I would assume I'm not allowed to carry it. What about, though, if it's in my mouth? For example: chewing gum or sucking a candy.
Would those be permissible outside where there's no eiruv? And if not, why?
There is a Mishna in Shabbos that says: "[If someone takes out with] his mouth ... he is not liable".
Tosefos asks on that from a Mishna in Krisos which says: "One could eat one thing and be obligated four Chatases... R' Meir said 'if it was Shabbos and someone carried, he is obligated.'"
Tosphos answers that the difference is that food is customarily carried in the mouth while other objects are not (if one carries something in a not-normal way one did not violate Torah law).
So carrying food in the mouth is a biblical prohibition. Carrying anything else in the mouth is a Rabbinic prohibition. Either way it is forbidden.
No, you cannot carry in your mouth either.