How do we know that at a time of 380.000 years, when CMB got free, the observable universe was not equal to the actual universe? Maybe they were roughly the same and couldn't that explain the horizon problem because then at 380.000 years the universe was just 380.000 light years wide and everything was causally connected up to that point, which could perfectly explain the uniformity. But obviously physicists always assume that the real universe was much larger than the observable universe. Why are they so sure?
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1$\begingroup$ The problem is, the universe might have been infinitely large from the beginning, in such a scenario the current or former observable universe is only infinitesimally large compared to the whole one. $\endgroup$– Pato GalmariniCommented Apr 23 at 3:36
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$\begingroup$ This video from Don Lincoln might help - Where did the Big Bang happen? $\endgroup$– mmesser314Commented Apr 23 at 4:05
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$\begingroup$ The CMB got free billions of years ago, when the universe was ~380,000 years old. $\endgroup$– PM 2RingCommented Apr 23 at 5:12
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2$\begingroup$ Why do you say that "380,000 years ago the universe was just 380,000 light years wide" ? $\endgroup$– PM 2RingCommented Apr 23 at 5:15
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It is possible in principle that the observable Universe is the entirety of the cosmic mass distribution. This would be really surprising, since it would place us right at the center of the Universe -- but it would be consistent with the bulk of established cosmology (just not inflation, obviously).
However, that does nothing to address the horizon problem. At the time of recombination (when the CMB last scattered), the radius of the observable universe was 42 million light years, while the particle horizon at the time was only 860 thousand light years. Here's how the two evolve with time.
The radius of the observable universe is -- by definition -- equal to the horizon size today. The observable universe is smaller in the past because of cosmic expansion. But the particle horizon is smaller still, because in the past, there was less time for light (or information) to travel.