So back to the Horizon Problem: how can it be that regions of the universe that are further away than light could have travelled during the finite age of the universe, have the same temperature and other physical properties?
The modern answer to this question is the theory of inflation. Basically, inflation suggests that the initial expansion of the universe did not look at all like the Hubble graph (previous post): instead the very early universe underwent an unimaginably large hyper-expansion right at the beginning. (Doesn’t this violate relativity, since nothing can travel faster than the speed of light? No, because relativity sets no constraints on space-time itself).
Inflation offers a simple solution to the Horizon problem – if the universe expanded arbitrarily fast, even the farthest flung points could once have been in thermal contact. Actually, inflation also offers a neat solution to the flatness problem: the maths shows that an inflationary universe would be driven towards flatness naturally (not unlike a balloon of unimaginable large suface area).
Of course, the above is a simplified overview of the theory of inflation – the main point is that if inflation is right, the universe was driven towards the critical value of flatness/ critical mass density that exists today (far from lucky coincidence). It’s also impressive that the theory was not posited to address the particular problems above, but rose in a completely different area of physics, namely Alan Guth’s attempt to address problems in Grand Unified Theory, a branch of particle physics