# Is the observable universe enclosed by an infinitely dense shell?

In modern cosmology, it is commonly stated to the public that as we look deeper and deeper into space, we are seeing further into the past. CMB is the relic of the big bang after photon decoupling following recombination. However, if we pushed further back in our conceptualization, eventually we get to the period of inflation, and then to a period before that where energy density of the universe was some large value (possibly infinite).

So why would it be wrong to conceptualize the universe as being enclosed by an infinitely dense shell?

Update: For clarification, wikipedia has a good definition of observable universe, and answers in the affirmative on how every observer will see a different observable universe. This question is whether there are valid approaches in theories to avoid issues of big bang singularites.

Update2: I scaled back the question and accepted an answer, I think I was being overly vague in the write up and plan on asking the question again.

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Infinite any quantity = very bad! Physicists do not like singularities. –  Noldorin Jan 16 '11 at 19:37
@Noldorin: No doubt, but not liking something isn't a reason. There must be some argument rooted in some theory as to why it is right or wrong. I think string theorists would argue starting with the characterization of event horizons. –  Humble Jan 16 '11 at 19:51
@Humble: My first comment was that infinite quantities are bad, if you missed that. By "bad", I mean are unacceptable in any effective physical theory. –  Noldorin Jan 16 '11 at 19:52
@Noldorin: So are you saying there are no acceptable physical theories? Certainly great efforts have been made to avoid, cut out and even "play shell games" in order to make our physical theories work, but most physical theories do contain singularities and yet we still accept them. –  Humble Jan 16 '11 at 19:59
@Humble: Only in the domain in which they do not apply. A singularity is a very direct sign that the theory does not apply to the concerned area. –  Noldorin Jan 16 '11 at 20:02

When we say "the Universe" without specifying "when", we usually mean the slice of our spacetime at a constant value of $t$, the proper time since the Big Bang (at each point). This "the Universe" has no boundary or shells. Quite on the contrary, it is pretty much uniform at long enough distance scales - above 300 million light years or so.

"The Universe" that has a shell on the boundary is a different slice through the spacetime, namely the past light cone with the tip at the Earth now. Approximating the spacetime by the Minkowski space for a while, this past light cone is composed of events $(t,x,y,z)$ that satisfy $$t=-\frac{1}{c}\sqrt{x^2+y^2+z^2}$$ where $t=0$ is identified with the present. Indeed, this past light cone is surrounded by a very thick and dense wall. But you can't say that this past light cone is "the Universe" now: it is a slice through spacetime that contains some places that are photographed now (those that are nearby) and some places that are photographed in a distant past (near the Big Bang, those that are very far).

So what we see is bounded by a thick wall - and we see lots of quasars at a very high redshift (big distance, big excursion to the distant past) and we also see the cosmic microwave background - from the times when the Universe was 350,000 years or so old. We actually don't "see" before that point using photons because the Universe was not transparent at all when it was younger than 350,000 years - it was full of plasma that was absorbing, emitting, and changing the direction of photons all the time. Using other probes, we can perhaps see before the point 350,000 years.

However, it's still more accurate to say that the "thick wall" doesn't appear at distant places of the Universe at one moment; instead, it appeared everywhere in the Universe a long time ago.

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What exactly do you mean by "enclosed by an infinitely dense shell"? Are you proposing to generalize the distant density in the past null-cone directions to all directions in 4D spacetime?

If you intend to imply that 13.7 bln years in the future a big crunch is awaiting us, I can tell you this is definitely incompatible with observations (accelerated Hubble expansion, etc.)

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Certainly am not implying a big crunch in any way, but when I look back in the past I see a "dense wall", so how do I remove it from my physical theory? –  Humble Jan 16 '11 at 20:37
There is nothing wrong with conceptualizing the big bang moment as a dense wall. But beware that this wall is infinitely redshifted (so in certain sense it is infinitely remote, and if we could look beyond the surface of last scatter we won't observe it as a 'hard' wall). –  Johannes Jan 16 '11 at 21:25