How would the universe look like without matter? I was wondering how the universe would look like if it would have been perfectly symmetrical in terms of matter and antimatter. If I understand correctly, there would be no "particle" but the energy released by matter-antimatter annihilation shouldn't just disappear, thus such universe probably wouldn't be an empty void. How does it differ from the current universe, apart from being deprived of persistent matter and related phenomena?
 A: Nothing new would replace the matter. Asymmetric matter was a tiny contribution to the energy density of the early universe, of order one part in a billion. Moreover, if we were to add the energy of the asymmetric matter to the primordial radiation bath, that would essentially just shift the exact same cosmic evolution to a slightly later time. An observer like us who arises from that cosmic evolution would arise at a correspondingly later time, so the added energy would make no difference to what they find.
So, would the universe be empty? Not quite. It would still contain the cosmic microwave and neutrino backgrounds, as well as a (potentially minuscule) primordial gravitational wave background. To the best of our knowledge, it would also still contain dark energy and dark matter. And indeed it would still contain essentially the same structure that we find today at scales larger than galaxies, except that structure would be composed of (almost) entirely dark matter.
Also, there would be some ordinary matter/antimatter in this universe. Its abundance would simply be low enough that a given particle is not expected to meet another particle to annihilate, even given the entire age of the universe. (In the field, we would say that these are thermal relics with an abundance fixed by freeze-out.) Specifically, the ordinary matter would be about a billion times less abundant than it is in our universe.
