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At which point in time in the history of our universe was the observable universe exactly as big as the entire universe? Does the Hubble Deep field represent such a time? Does this question make sense or am I forgetting that the observable universe grows directly proportional to universal expansion?

Qmechanic
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Hayk Amirbekyan
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  • There is no direct evidence of the whole universe being larger than the observable universe. This is an unproven theoretical conclusion of the current Friedmann cosmology that is becoming increasingly problematic. – safesphere May 21 '20 at 03:59
  • While I agree about the current lack of direct evidence, there's indirect evidence in the combination of the resemblance between the cosmological horizon and the horizons of black holes, with the astrophysical evidence for black holes (mainly the elliptical orbits of stars whose partner--most stars being in binary pairs--has disappeared by collapsing into one), together with the intractability of the singularity problem. The latter's resolved hypothetically thru multiverse cosmologies dependent on such causal separations as horizons, cf. Nikodem J. Poplawski's on Arxiv. – Edouard – Edouard May 30 '20 at 19:53

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Even assuming a finite (positive curvature) universe the observable universe consists only of that part of it from which light can reach us in the time since the big bang. This diagram from my book may help. The observable universe is represented by the white region in the core.

enter image description here

If the universe is infinite there will always be parts of it outside the finite region from which light can reach us in finite time.

If it is finite, there can become a time when light can reach us from all parts of the universe. The time is model dependent, but in the idealisation of a matter only model, with no cosmological constant, this will be at the point of maximum expansion, at which point the universe starts to contract leading to a big crunch (in practice it will be a little later because of radiation).

Charles Francis
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    It might be useful to note that the experimental evidence currently points to the universe being infinite (measured curvature is indistinguishable from zero). – probably_someone May 20 '20 at 20:38
  • The “infinite” universe has no physical meaning. Sadly this misconception is common. – safesphere May 21 '20 at 04:11
  • @probably_someone. There are other interpretations consistent with observation, but this is not the place to discuss them https://arxiv.org/abs/1603.02568 – Charles Francis May 21 '20 at 04:55
  • @safesphere. I agree, but this is not the place to discuss it. See my books. – Charles Francis May 21 '20 at 04:56
  • Or see the related questions, such as the one (giving hypothetical time frames for changes in the CMB data) at https://physics.stackexchange.com/questions/296649/what-evidence-is-there-that-the-big-bang-was-not-just-a-local-phenomenon?rq=1 – Edouard May 30 '20 at 19:38
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    @Edouard, as it happens that was not a related question. That was question from someone claiming to be a mathematician who did not think it was necessary to understand the maths before criticising it. For genuine criticisms of the standard model of cosmology, see my books. As I have already said, this is not the place to discus them. – Charles Francis May 30 '20 at 20:26