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Two things we take, for this purpose, to be axiomatic:

  1. The CMB is the oldest thing we can observe directly
  2. The cosmological red shift tells us how "old" something we are observing is

Yet we also have a third axiom:

  1. There are some parts of the universe we can never observe because they are receding away from us at a superluminary speed.

But this surely also implies that we can see beyond the CMB if we see anything which has a red shift indicating an expansion speed very close to $c$.

This suggests axiom 2 is incorrect - so what should it be instead?

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    $\begingroup$ Stuff is receding from us at superluminal speeds well before you hit the CMB, actually. Looks like this article would explain that: arxiv.org/abs/astro-ph/0011070 $\endgroup$ – zibadawa timmy Nov 17 '14 at 1:46
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    $\begingroup$ I think this question is very confused. Even if CMB is the oldest radiation we can observe, does NOT mean that its redshift is still the same as the one when it has been originated. I do not really understand the late statement of the question. Any clarification? $\endgroup$ – Py-ser Nov 17 '14 at 3:27
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Yet we also have a third axiom:

  1. There are some parts of the universe we can never observe because they are receding away from us at a superluminary speed.

This is simply false, so of course it gets you in trouble if you insist on taking it as axiomatic. The average recession velocity goes luminal at redshift $z\approx 1.4$, while there are observed galaxies and objects at $z\sim 8$, e.g., Z8 GND 5296 dwarf galaxy and the GRB 090423 gamma ray burst. Additionally, there are at least some candidates for objects much farther than even that, possibly $z\sim 12$.

That means that other than the CMB itself, the most distant and most ancient object we might have observed hails from when the universe as around $370\,\mathrm{Myr}$ old, which is around a thousand times older than the recombination epoch when the universe first became transparent and hence when the cosmic background radiation was emitted. In terms of redshift, the CMB has $z\gtrsim 1100$ or so.

But this surely also implies that we can see beyond the CMB if we see anything which has a red shift indicating an expansion speed very close to $c$.

Something at redshift $z\gtrsim 1100$ has a recession velocity of $v\gtrsim 3.2c$.

This suggests axiom 2 is incorrect - so what should it be instead?

Since (3) says incorrect things, it's best to throw it out instead.

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