It is very hard to predict since most of the predictions have to do with events that happened in the universe at its 'birth'. I would hope that such a theory would give the definitive inventory of the kinds of particles and fields that contribute to the gravitational field of the universe. It would explain the cosmological constant and what happened to it today. It would not tell us if the universe is open or closed because that is still something that has to be decided by direct observation. If it is a testable theory, it should have some exciting things to say about the fundamental nature of space-time, why it has 4 dimensions, why certain laws of physics seem favored, and why there are fundamental constants in the universe. Beyond that, I have no great expectations for such a theory other than as it completing a unified description of how the elements in our physical universe operate the way that they do. This is not strictly a cosmological issue.