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This is a little embarrassing but I don't understand how the inflation model solves the horizon problem.

My doubt is the following: What does the occurrence of an exponential expansion of the early universe has to do with the Cosmic microwave background (CMB) homogeneity since those photons (that compose the CMB) correspond to a much latter epoch and were emitted from regions that at that time were already causally disconnected?

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    $\begingroup$ One can argue that the horizon problem is artificial and not an actual problem of its own, at all. The temporal homogeneity of the universe pales in comparison to the homogeneity of its physical constants. We now have about two dozen parameters in the standard model that we treat as perfectly matched, as if that was somehow natural and one cosmological quantity that is just mostly matched, which we get very upset about. I would suggest you put the horizon problem into that perspective, and treat explanations for it accordingly. $\endgroup$
    – CuriousOne
    Commented May 11, 2016 at 0:01

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The argument is that

(mixing happens) => (inflation happens) => (mixed regions are out of causal contact, but have no way to change their local temperature)

In this scenario, it doesn't matter when the photons are emitted. Their apparent homogenity is an effect of the left most step.

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    $\begingroup$ Let me see if I understand, so, you are saying that the early universe is anisotropic, then we have an inflationary epoch. After that epoch the observable universe of a given observer (at a certain point) would be composed of points that were very close prior to inflation, such that any anisotropies in their physical properties would be very small (since they were so close previously)? $\endgroup$
    – PML
    Commented May 10, 2016 at 22:15
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    $\begingroup$ I would say you understood the answer correctly. $\endgroup$
    – Yukterez
    Commented May 11, 2016 at 0:47
  • $\begingroup$ @PML: yes, that's right. $\endgroup$
    – Zo the Relativist
    Commented May 11, 2016 at 1:52

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