You're right: the "Observable Universe" is defined only relative to a point of observation. For any spot in the Universe, there's a 93-billion-light-year-wide sphere centered about that point that constitutes the OU for that point. What exactly this sphere means it somewhat complicated. The simplest way I can think to say is this: The radius of the OU is the current distance of the farthest point in space such that if a radio signal were emitted from that point 13.7 billion years ago, immediately after the Big Bang, it would be possible in principle (but by no means in practice) for us to receive that signal. Anything that is outside of the OU is causally disconnected from us as a matter of fundamental principle, and nothing that has ever happened or ever will happen at any point outside the OU can ever affect us in any way, ever.

It was previously (up until a decade or so ago) an open question as to whether the Universe itself might be smaller than the OU. This sounds absurd, but consider the example of a hypothetical jet that could circle the Earth ten times without refueling. While normally the "range" of a jet plane is a circle about some point, the range of this jet exceeds the size of the Earth itself. Similarly, if the Universe were smaller than the OU, some of the distant galaxies we see would actually be repetitions of closer galaxies from an earlier time and a different angle, since the light had been "looping around" the Universe once or more before reaching us. Or, as Modest Mouse put it in one of their better songs: "The Universe is shaped exactly like the Earth / If you go straight long enough, you end up were you were." Recent evidence from the Cosmic Microwave Background has made this idea very unlikely, but it's a useful example to clear up misconceptions about the OU.

So, however big the Universe actually is, it's bigger than the OU, which means that the stuff cosmologists are debating about is space that cannot, even in principle, ever be observed. It's an important question, though, since whether the Universe loops back on itself on the large scale or just keeps going forever has implications for whether gravity will win out over Hubble Expansion in the long run, determining the eventual fate of the Universe.

I'm really curious about how CBR observations solved the question related to universe size.

Also, then, for me this makes me wonder: is then the big bang simply the origin of the null cone over whose event horizon we can't see? Clearly this is a Minkowski spacetime paradigm, and I have no idea where that stands in terms of general favor.

Also: further reading? I'm guessing "The large scale structure of space-time" is a bit dated ;)

The WMAP space probe allowed better measurements of the CMBR, from which the relative composition of matter at the time of the CMBR's emission could be determined (using methods I don't fully understand). Once it was known that the Universe was X% atomic nuclei, Y% photons, Z% dark matter, etc., this information implied certain bounds on how quickly the Universe was expanding during the inflationary epoch (10^-36 to 10^-32 sec after the Big Bang), since high rates of expansion can overpower the nuclear forces and prevent quarks from bonding to form protons/neutrons. The math for all of this is, unfortunately, far over my head. Sorry I can't be of more help.

I'm not fully understanding your next question. The origin of our light cone is here and now. Minkowski spacetime is an approximation that (almost) works in the absence of gravitating bodies. Once general relativity gets involved, certain features of Minkowski spaces start failing, like the fact that you can always reorient light cones so that they're parallel. This fails even in intergalactic space, where there is still a non-vanishing Weyl tensor effect due to Hubble Expansion. So, without getting too much into the detail, in the real world light cones are (forgive me) uncannily un-coney. Our past light "cone" collapses back in on itself in the distant past and converges on the Big Bang, but so do light cones everywhere in the Universe, even outside of our observable universe. Though, whether a light cone even has meaning before the inflationary epoch is a question of Grand Unification Theory, which is very much over my head.

As for further reading, Dodelson's "Modern Cosmology" is great if you're not afraid of learning the math behind General Relativity: http://amzn.com/0122191412 The text doesn't assume very much familiarity with GR, but it does assume enough mathematical sophistication that you can fill in any gaps in your knowledge on your own.

(And if you don't like the idea of learning about tensors, you're SOL. Sorry. There's a very low ceiling of how much one can know about cosmology without tensor calculus.)

Whoa, I praise your deep knowledge of cosmology, anyway, to my question:

> "So, however big the Universe actually is, it's bigger than the OU, which means that the stuff cosmologists are debating about is space that cannot, even in principle, ever be observed"

What if we learn how to make better neutrino telescopes, them how much of the Unobservable Universe could we see? Can you recommend a paper about this?

The stuff outside the OU cannot be seen in principle. Its size is fully independent of our current level of technology, and no advancement of technology will let you see beyond it. (Seeing beyond it would mean you can send signals faster than light, which implies you can build a time machine, in which case all bets are off.) In practice, we cannot see anywhere near as far as the radius of the OU, since after a certain distance you're looking so far into the past that space is opaque to microwave radiation. If you can somehow see neutrinos you get to see more, but that's still all inside the boundary of the OU.

Yes, I know that they cannot move faster than the speed of the light, and that the universe was opaque to visible light before the decoupling of radiation.

But there're a group of neutrinos that decoupled before the decoupling of radiation, even before this gravitational waves were at large in the universe, they could in principle say something about regions that are outside the Observable Universe, this ignoring the fact that they must be absolutely difficult to observe and that both neutrinos and gravitation waves are generated by new events and that we can in fact extract some information about these regions from them in the same way we can from light.

This was what I found from a paper, "Detection of gravitational waves with resonant antennas" from Francesco Ronga, earlier today:

"Gravitational wave and neutrino astronomy will increase the amount of observable universe, because they will investigate places that are completely inaccessible to the electromagnetic radiation and probably will change our knowledge of the universe evolution"

I think you're confusing two very different points in the history of the Universe. The CMBR was emitted after the decoupling of matter and radiation, as you mentioned, but this event was over 300,000 years after the Big Bang. And you are correct that there could, in principle, be observable signals emitted before this event in the form of neutrinos or gravitational waves. The observable universe, however, is defined not by reference to the signals emitted at the decoupling event, but rather the start of the inflationary epoch, which was merely 10^-36 seconds after the Big Bang. So, the OU is big enough that it encompasses all of the space from which any signal, even neutrino or gravitational, that might have been emitted 13.75 billion years earlier that could eventually reach us.

But, terminology aside, this still leaves your question: How much farther could we see if we could pick up neutrinos or gravity waves? Not a whole lot, unfortunately. Most of the expansion of the early Universe occurred during the (aptly named) inflationary epoch, and that lasted less than a tiny fraction of a second, leaving very little time for a neutrino or gravitational wave to travel before the Universe became very large. The expansion that occured in the following 300,000 years is negligible by comparison to that first tiny moment, so you won't get a whole lot more than 300,000 light years out of those neutrinos. I'm too tired and lazy to do the math to find the radius of the surface of last scattering, so I'll run a quick Google search, and...

The final answer is that the visible universe, or that which is not obscured by the opaque matter that dominated in the first 300K years, is a sphere with radius of 45.35 billion light years, while the observable universe, which is everything that can observed in principle, is just a bit further at a radius of 46.5 billion light years. So, yeah, we've got most of it covered.

You are correct. There's more to the universe than we can see, but what we can't see should be basically the same as what we can. By analogy, from any place on the earth, you can only see as far as the horizon[1]. If you were to teleport (or travel) to the edge of your horizon, you would see more earth that you couldn't see before, but that new stuff would basically be similar to the earth you're seeing now.

Just for kicks, let's add in that the earth is expanding like the universe. You're at point A, there's a tree at point B, and the horizon past the tree in that direction is point C. If the earth is expanding, then point B will be receding from both point A and point C, in part because point C is receding twice as fast.

[1] The reason for the boundary of the observable earth is totally different, but that doesn't change the point.