Imagine you have a box of black body radiation. What happens if you open the box for a long time? It becomes dispersed and no radiation remains in the box.
Now, apply this example to the Cosmic Microwave Background radiation. The CMB has been produced about 380,000 years after the Big Bang. Giving that the space is flat as many observations suggest, that radiation has been produced in a universe with no boundaries.
Now, my question is this: in these conditions, why that radiation has not been dispersed completely so far? It is true that the radiation has been produced everywhere in the space but giving that the space is infinite, why has not it been dispersed do far?
Calculations in the standard textbooks are done in such a way as if the CMB has been within a physical box, however expanding with the universal expansion. But, this is not the actual situation. The CMB has not been and is not enclosed by walls of a box, so it must have completely dispersed so far. What has prevented this to happen?
Answer
The CMB was emitted from everywhere, in all directions. The CMB emitted at the point where you are standing right now, has now been dispersed to a distance $d_\mathrm{CMB}$ equal to the distance that light can travel in the almost 13.8 billion years that have passed since it was emitted*.
(note that $d_\mathrm{CMB}$ is much larger than 13.8 billion lightyears, since the Universe has expanded since it was emitted; in fact it's roughly 46.5 billion lightyears.)
On the other hand, the CMB emitted from a distance that is now $d_\mathrm{CMB}$, is what we observe today. That means that the CMB we observed today all comes from a thin shell of the Universe in which we are centered, and which has a radius of $d_\mathrm{CMB}$.
The drawing below may help understand; in a while from now, the picture would look exactly the same, except $d_\mathrm{CMB}$ has increased so that the sphere will be larger, since by that time, photons originating from farther away will have had the time to reach us.
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