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The horizon problem states that because of the speed of information can't be faster than light and the distances between far regions are too big there is a problem because they look quite the same. Therefor, the inflation is introduced. But what I don't understand is why those regions can't be the same without inflation or something like that? They have the same origin and the universe was in the beginning too empty to make a difference for the direction you went. So in my simple understanding, it is rather expected that they should be the same but why are cosmologists think different about that?

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  • $\begingroup$ Not sure if I got you right, but I think that's the case. Those regions $\textit{are}$ the same. To explain that, they had to be connected somehow in the past. Calculating backwards linearly from now wouldn't yield in the Big Bang. There had to be a period where the universe rapidly expanded. $\endgroup$ – rtime Feb 14 '16 at 20:34
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We don't really know what happened at the time $t=0$. It doesn't really make sense to say that everything "touched each other" at $t=0$, particularly if the Universe is infinite. But we can calculate the distance that a photon — and hence the maximum distance that any information — can travel in the expanding Universe in a given time. This calculations depends only on the Hubble parameter, and the densities of the various components of the Universe, and whether you start your calculation at $t=0$ or $t=10^{-12}\,\mathrm{s}$ makes little difference after a second.

The answer is related to your previous question about the cosmic event horizon which was also about the particle horizon, i.e. the distance that light has been able to travel since the Big Bang. If you were present when the CMB was emitted, you could also calculate your particle horizon. It would of course be much smaller than today, since light at this time had only traveled for 380,000 years. If the Universe hadn't been expanding, this horizon would of course be 380,000 lightyears, but due to the expansion, it is quite a lot larger, roughly 850,000 lightyears.

This means that, at the time of the CMB, regions farther apart than 850 kly had not had the chance to be in causal contact.

We can also calculate how large an angle 850 kly at the CMB would suspend if observed today. It turns out to be 1.7º. That is, if the Universe had just been expanding like we observe its expansion today — i.e. depending only on the densities of the known components — patches on the CMB map separated by an angle $\theta > 1.7^\circ$ shouldn't look the same.

But they do.

Inflation solves this problem by saying that the Universe initially went through a much, much faster expansion, such that regions much, much farther apart than the 850 kly have been in causal contact. Still, even with inflation, the particle horizon is not infinite. So on scales much, much larger than the observable Universe, it may be inhomogeneous.

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  • $\begingroup$ You say : It doesn't really make sense to say that everything "touched each other" at t=0t=0, particularly if the Universe is infinite." But that is just my point, I can't see why it is not making sense. Fe usually when an electron is scattering his electic field it is in all direction the same, isn't it? So why not in case of a singularity like the primeval atom? $\endgroup$ – Marijn Feb 15 '16 at 9:49
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    $\begingroup$ I'm not sure I understand completely your last two sentences, but the reason I'm saying it doesn't make sense is that we can calculate "backwards" and say that so-and-so long ago, these two points were that close, and even longer ago, they were even closer, and you can go on calculating this for any finite $t$ (although before t ~ 1e-12 s it becomes increasingly more speculative). But you can't say what happened at $t=0$, because no theory describes this time. And, if the Universe is infinite, it has always been infinite, so there must be points that were always far apart, even at $t=0$. $\endgroup$ – pela Feb 15 '16 at 10:36
  • $\begingroup$ hmm, points 850 kly were out of reach, but regions? $\endgroup$ – adrianmcmenamin Feb 15 '16 at 10:56
  • $\begingroup$ @adrianmcmenamin: Yeah well, maybe this is a bad language (I'm not English), but what I mean is that if [the closest points of] two regions are farther apart than 850 kly, they are causally disconnected. If they are a tiny bit closer, then a tiny bit of the regions are connected, but the rest is disconnected. And if they're so close that their far sides are closer than 850 kly, then the whole of the regions are connected. Does this make sense? $\endgroup$ – pela Feb 15 '16 at 11:26
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There is a fundamental (but disputed) idea in Cosmology called "the Cosmological Principle" (see https://en.wikipedia.org/wiki/Cosmological_principle) which states, at a sufficiently large scale, the universe looks the same everywhere at the same epoch. And there is a lot of evidence to suggest that it does.

However the inflation theory states that very small, quantum level, variations in the universe a very small time after the Big Bang should be reflected in observations of the universe at a large scale today because inflation means that these parts of the universe never had time to exchange information (or photons) to equalise their energy in the very earliest moments.

As an analogy (perhaps a bit strained) - if you had a room in which there was a radiator giving out heat and then the radiator was switched off, after a few hours you would expect the temperature in the room to be the same everywhere, because the warm air would mix with the colder air and the temperature would equalise. But imagine if there was some sort of barrier of distance between the warm parts and the cold parts - then the cold parts would stay cold and the warm parts would stay warm for much longer.

The task cosmologists have set themselves is to find the imprint of these patterns in the density of the observed universe (as energy and mass are equivalent the hotter/more energetic parts of the early universe should have a bit more mass in them today).

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    $\begingroup$ This doesn't answer the question as to why inflation is needed to causally connect points larger than their particle horizon. $\endgroup$ – pela Feb 14 '16 at 22:38

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