So far I have been sweeping the worst confusion under the rug.
First off, when we talk about "the Universe today," we mean "what we see today." This isn't quite fair, since the light we detect from distant objects was emitted a long time ago, maybe almost at the beginning of time! We have no way of knowing, even in principle, what those objects have been up to since then. Maybe they are all gone by now.
This creates a problem with energy conservation : since every star is in a different inertial reference frame from every other, what is simultaneous for one is not for another; in that case, how does one talk about energy conservation on a Cosmic scale? When do the books get balanced, according to whose perspective? I don't know of any resolution for this confusion. Perhaps energy conservation is an obsolete concept on the large scale.