A great list of Cosmology Questions Answered, including: Why do we think that the expansion of the Universe is accelerating? What is quintessence? What is the Universe expanding into?
Everything that we measure is within the Universe, and we see no edge or boundary or center of expansion. Thus the Universe is not expanding into anything that we can see, and this is not a profitable thing to think about. Just as Dali’s Corpus Hypercubicus is just a 2-D picture of a 3-D object that represents the surface of a 4-D cube, remember that the balloon analogy is just a 2-D picture of a 3-D situation that is supposed to help you think about a curved 3-D space, but it does not mean that there is really a 4-D space that the Universe is expanding into.
