Online Astronomy eText: Galaxies and the Universe
The Observable Universe
(brief notes about a vast topic)
 The following is an answer to a question about the size and expansion of the Universe. As time permits I will alter its structure so that it becomes a stand-alone discussion, but for now it is presented as-is. The reason for this post, aside from its general interest, is that some of the topics covered here are not always correctly presented, even by astronomers (that was in fact the point of an interesting Scientific American article of a few years ago).

 What is the size of the Universe (in light years)? Is the size of the Universe expanding, and if so, at what rate? Will it continue to do so, or will it stop at some point, then begin to contract?

 There are some complications involved in answering your question, so a simple answer isn't necessarily correct, and a correct answer may be more complicated than you want. So I'll start with simple statements and expand on them.
 (1) The size of the Universe is not known, but is thought to be hundreds or thousands of times larger than the size of the "observable" Universe, which is the portion small enough that light has had time to get from "there" to here. The radius of the observable Universe in light years is therefore considered to be the same as its age in years, or a little less than 14 billion.
 (2) Both the overall and observable Universes are expanding. The observable Universe is expanding at one light year per year, because we can see that much further each year. The overall Universe is expanding much faster than that, depending upon how much bigger it is.
 (3) The local rate of expansion of the Universe is now roughly constant, at about one light year of expansion for each light year of distance over a period of about 10 billion years, and should remain near that value for the rest of eternity. So the Universe will expand forever.
 (4) Although the rate of expansion of the observable Universe is constant at one light year per year, and the local rate of expansion is more or less constant at one light year expansion per light year of distance per 10 billion years, the rate at which individual objects move away from us is accelerating, because they are getting further away from us. An object now 200 million light years away is moving away from us at about 200 million light years per 10 billion years. But in 10 billion years it will be 400 million light years away, and since it will be twice as far away as now it will be moving away from us twice as fast. In other words, the local rate of expansion is constant, but distant objects move away from us faster and faster over very long periods of time.
 (5) The discussion in (4) only applies to things that are far away. Things less than a few tens of millions of light years distance (such as the local supercluster) are gravitationally bound, and do not move away from us. They will always be about the same distance from us that they now are. But in the very distant future, all things beyond that "nearby" region will be unimaginably far away, with the space between us and them expanding at a total rate faster than lightspeed, and the observable Universe, though much larger than now, will be completely empty save for the gravitationally bound region close to us.
 (6) When we say that the observable Universe has a radius in light years equal to its age in years, that is based on the idea that the light must have been traveling that long to get here. But since the Universe was expanding while the light traveled, the distance it has had to travel is larger than the distance between us and its source at the time the light was emitted. So the most distant observable regions were only about half the 14 billion year distance quoted in (1) at the time the light we now see left them.
 (7) As a corollary to (6), the objects which we now observe at the "edge" of the observable Universe are now well beyond the 14 billion year distance, moving away from us at more than the speed of light, and we will never see the light they are now emitting, because the space between us and them is expanding faster than light can travel through it. This is why in (5), the contents of the observable Universe seem to shrink over time, even though its size increases.
 (8) Note that in any discussion of faster-than-light expansion, the speed-of-light speed limit is not violated. That only applies to the motion of light or physical objects through "local" space. There is no limit to how fast the empty space between distant objects and us can expand; it just depends on how far away they are, and the local rate of expansion. The latter is constant, but as noted in (4), the former is increasing at an accelerating rate.
 (9) Finally, for now, all the above has to be modified for regions moving away from us so fast that they have an expansion speed close to the speed of light, and slightly modified for regions closer than that. Such distant regions are "foreshortened" by their rapid motion away from us, so that the actual distance between one part of the very distant observable Universe and a still more distant part is larger than their separation as measured by us.

 As an example of how corrections for the expansion of the Universe alter our perception of things, consider the quasar 2QZ J000827.4-295423 (so-called because its J2000 position is RA 00 08 27.4, Dec -27 54 23). As noted at the linked entry, based on a redshift of z = 2.061, 2QZ J000827.4-295423 was about 5765 million light years away at the time the light by which we see it left it, 10570 million years ago. During that time the space between us and the original position of the quasar expanded by about 4800 million light years, causing a 4800 million year delay in the light's arrival. Throughout the 10570 million years it took for its light to reach us the expansion of the intervening space carried the quasar to even greater distances, and it is now about 17650 million light years away. As a result the space between us and the quasar is expanding at a cumulative speed far greater than the speed of light, and any radiation now being emitted by it will never reach us, so although we see it at a time (10570 million years ago) when it was still part of the "observable" Universe, it has now moved outside that region.