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There are three things I can imagine happening:

  1. It appears one light year further away every year, which would be a bit weird, because it would be behind the universal event horizon, but still visible. It would appear completely unaffected by the Big Rip (which might be understandable, because it's in the past). And in the far future you would only see Milkdromeda, then a loooooooooot of nothing and then the cosmic background radiation. Also, what would prevent you from seeing things that happened shortly after the universe became transparent?
  2. It disappears behind the universal event horizon, which would be weird, because it was everywhere. Could there be anything preventing the photons emitted back then from reaching far future observers?
  3. It appears to get closer, matching the seemingly shrinking universe (from universe to galaxy to solar system…). This variant might appear the least weird to far future observers ("That's just how big the universe is, there is nothing beyond it."), but I see no reason why it should appear to shrink.

Is it any of these? And why?

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The radiation background is everywhere - take any volume of space, and you will find photons of the CMB moving through it in all directions.

What happens when the universe expands is that the radiation is redshifted. The temperature is inversely proportional to the scale factor of the universe: $T\propto \frac{1}{a(t)}$.

In a big rip scenario $a(t)\rightarrow \infty$ as we approach $t_{rip}$. So the CMB temperature quickly goes down to zero.

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  • $\begingroup$ Ah, interesting. But as long as you can still measure it, it appears further away, like in my scenario #1, right? Or is there something different with bent space or something like that? $\endgroup$
    – Fabian Röling
    Feb 23, 2019 at 20:43
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    $\begingroup$ It is like a rainbow: you see it projected on your sky sphere, but in practice the light in the rainbow was refracted from raindrops between you and the sky sphere. The CMB photons are everywhere and move in random directions, so you see it as a isotropic field in all directions and it looks like it is far away. $\endgroup$
    – Anders Sandberg
    Feb 25, 2019 at 14:16

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