My question relates to the estimated size of the Universe. Please excuse my rough numbers but I've seen estimates for the age of the Universe of 12 billion yrs +/- and some estimates for the physical size of the universe of 10-15 Billion light years in radius (or at least to the farthest visible galaxies). For this size measure, even if the light was emitted near the big bang origin and had close to the life of the universe to expand, the source would have had to expand at near or beyond the speed of light for the entire life of the universe to achieve that size.
Since we know that the universe is expanding at a rate that is a fraction of the speed of light and that this rate was even slower in the past since it is accelerating apart, how could it be possible that the physical universe could have achieved such an enormous size?
Your confusion arises from a common misconception that you have about the Big Bang. It's incorrect to think of the Big Bang as an explosion which happened in a particular place inside an otherwise empty universe; in fact, the big bang happened *everywhere*.
To explain what the Big Bang actually *was*, let's examine why the misconception is wrong. Imagine a universe that was completely empty, in which an explosion occurred somewhere, sending the galaxies outwards. (note that this model has *never* been seriously considered by astronomers, even though it's what people normally conceive of when they hear the phrase "Big bang.") In this case, we would be located on one of the many galaxies on an expanding shell of gas surrounding the center of the universe: the location of the Big Bang. In such a universe, there are two important regions: one completely empty region surrounding the gas cloud into which the galaxies haven't had time to expand, and one region near the center filled with gas, galaxies, etc.
Since we would be on the expanding shell, this would theory predicts that an entire half of the sky (the half facing away from the BB) should be empty of other galaxies. Moreover, the most nearby galaxies should be found when we look in a direction tangent to the shell, and the most distant galaxies will be found when we look down into the shell. In addition, we would never be able to see the Big Bang itself, because the light from the explosion would have passed us by long ago.
This is not, in fact, what we observe. Galaxies, nearby and far away, are found in every direction equally. In any direction you look, you see both nearby galaxies, and galaxies that are 13 billion light years away. All of these galaxies are moving away from us, and the farther they are from us, the faster they recede. The speed of their recession is exactly proportional to their distance from us, so that if galaxy A is twice as far away as galaxy B, then A recedes twice as fast as B. This is not the behavior of an expanding shell. Moreover, if we look 13.7 light years distant, we see the redshifted glow of the Big Bang itself, in contradiction to the predictions of the expanding shell model. Therefore, the "Expanding shell" misconception cannot be correct. A theory of the universe must be one where all of space is uniformly filled with galaxies, in such a way that the BB is visible, as it is observed to be.
The real Big Bang theory is a little more difficult to get your mind around, because there is simply nothing like it on Earth. But imagine a 2-D universe set out on the top of a trampoline made out of stretchy material. Cover the trampoline in little paint-marks representing the galaxies, and fill the trampoline area uniformly with these galaxies. Now, real trampolines have edges, but not the universe. So now you have to imagine the trampoline as either being infinite in size (an "open" universe), or finite and curved back apon itself into what looks like (to an outside observer) a sphere (a "closed" universe).
Now, the trampoline material itself is space-time, and the paint marks are galaxies. Note that even though you imagine the trampoline "embedded" in a real 3-D space, an imaginary ant astronomer on one of the galaxies could never see anything that wasn't on the trampoline. Light travels through space, and space is the trampoline material itself. There is left-right and back-forth in the trampoline universe, but no up-down. Up-down doesn't exist AT ALL in the trampoline universe: you may have heard of "flatland." This is it.
Now, any ant-astronomer on the trampoline can look in any direction he chooses, and will see galaxies uniformly in all directions around him. Great. That's what we want. But what about this "expansion" business? Aren't all the galaxies streaming through space? Well, actually, no. That's why I had you *paint* the galaxies on the trampoline. They don't actually go anywhere. Space expands around them.
Imagine that the trampoline itself is stretching larger and larger. (If you're having trouble imagining an infinitely large trampoline getting bigger, simply imagine that the edges are too far away to see.) The distance between each and every one of the paint splotches gets bigger and bigger--- without any of them moving across the face of the trampoline! In fact, the paint-splotch galaxies appear move away from each other because more space (trampoline material) is being created in the spaces between them.
Indeed, the farther two galaxies are from each other, the faster the distance between them increases, in direct proportion! If the trampoline stretches to twice its original size in (say) one second, then two splotches that were originally 1 cm apart are now 2 cm apart... an average speed of 1 cm per second. Two splotches that started out 2 cm apart are now 4 cm apart... an average speed of 2 cm per second! This is what we mean by the "expansion of the universe:" it's the *space itself* between the galaxies that is expanding.
An ant astronomer presented with such an expanding universe would observe all of the other galaxies expanding directly away from *him*, regardless of which paint-splotch he was standing on. All ant astronomers observe that they are the "center of expansion." Such an astronomer would hypothesise that if the distances between paint-splotches are increasing now, then they must have been smaller in the past. In fact, there must have been a time in the past when the distances between all the (finitely distant) galaxies he can see was zero: the Big Bang. Where did the Big Bang happen? Everywhere! Every single bit of trampoline is involced in it, and the trampoline is all the space there is.
Moreover, the ant astronomer sees the Big Bang, too. If he calculates that the BB occurred 10 minutes ago, then light has only had 10 minutes to make it to him. If the ant looks out to a distance 10 light-minutes away, he'll see those galaxies as they were 10 minutes ago--- as the hot, boiling gas of the Big Bang! If he tries to look further than that, he sees nothing, as light from those regions has not had time to get to him.
Our own universe is a 3-dimensional analogue of the trampoline. Space itself between the galaxies expands, and we see galaxies, near and far, in all directions. The universe is either open (infinitely large, so that an astronaut in a rocket can travel as far as he likes in any direction and never reach the edge) or closed (finite in volume, but an astonaut heading off in a given direction eventually circumnavigates it and returns to his starting point). A travelling astronaut always observes the galaxies expanding directly away from himself, regardless of his position. All observers observe the galaxies in uniform motion away from themselves, with speeds in proportion to their distances.
So to answer your question: the *observable* universe is exactly as large as it is old. If the universe is 13.7 billion years old, we can observe out to 13.7 billion light-years. At that distance, our view is obscured by the Big Bang. In reality, the *whole universe* is much, much larger than that (possibly infinitely large), but we cannot observe the vast majority of it, because light has not had time to reach us yet.
Answers provided by HSU Astronomy Professor David Kornreich.