I don't mean to be flippant but I have never understood why the homogeneity in the universe needs.explaining. I have searched other questions on stack exchange and they don't really address the question. I am going to ask.
Say a bunch of identical particles are created contained in a void of absolutely nothing. They are endowed with a set of quantum laws and the quantum mechanics is deterministic. Initially, they are in thermodynamic equilibrium. They begin to expand so fast that they break into regions that are causally disconnected. Then each of these regions is identical, has the same set of laws and zero external influence by definition. Surely they are each essentially an initial. value problem with the same start conditions. Mathematically they should all evolve the same, shouldn't they? Even if QM were not a deterministic theory, these regions are identical, isolated and have the same laws. How could they evolve differently? And, unless they either have different sets of laws, different starting conditions, or some differing external influence from another source, how could they ever be different?