Is the total enthalpy of the universe constant?
It would seem like the answer would have to be yes, since (1) enthalpy change represents the heat exchange between the system and the surroundings, and there is nothing "outside" the universe, and (2) in the equation $H = U + PV$, the matter in the universe is surrounded by a vacuum so $P = 0$ and that term disappears, so the enthalpy is just the internal energy $U$ of the universe, which never changes by the law of conservation of energy.
But I can't find a reliable source confirming this explicitly. (The only place I can even find this question posted, is on Quora:
and the only yes/no answer says: "No, if this was the case, our school books would have ended up with another law of conservation of enthalpy", and that's why I don't read Quora.)