Before discussing the intended topic, the reader needs to understand the idea of the Hubble radius. This explanation will remain non-technical, but necessary to comprehend the "real" topic.

The Hubble radius describes the current size of the universe, based on the (reasonable) assumption that light from a point-source origin of the universe (ie, the big bang) travelled radially outward from that point.

Simply put, anything the big bang threw out can only have travelled, at the speed of light, a certain finite distance. Our universe, therefore, consists of a perfect sphere having a radius the exact distance that light can travel since the big bang, roughly 12 billion light-years. No more (which would require something to travel faster than the speed of light), and no less (since the big bang did emit quite a lot of energy in the form of light, that light can only have gone radially outward at the speed of light).

This idea of a forced radius of the universe due to light travelling outward works both ways, however. Considering it from the opposite direction gives rise to the idea of the causal horizon.

Most people realize that light from distant objects takes some time to reach us. The light we see from our sun takes just over 8 minutes to reach us. This means we actually "see" the sun as it existed 8 minutes ago, not as it stands "now". As we get further away, this seeing-into-the-past effect grows larger - Sirius, the brightest nighttime star in our sky, lies 8.7 light-years away (fairly close, for a star), meaning that we see it as it existed 8.7 years ago. Quite a lot further away, we can see quasars near the edge (as defined by the Hubble radius assuming a universe roughly 12 billion years old, of course) of our universe, roughly 10 billion light-years away.

Now, imagine the existance of something that did not result from the big bang. Given the speed of light as the fastest rate at which information can travel through space, in order for us to detect such an object, a certain amount of time must have passed, just like it must for the sun, Sirius, and those quasars. But consider the quasars - At their distance, it took 10 billion years for their light to reach us. Something even further from us would take a proportionately longer time before we could see it. What happens when it would take longer than the age of the universe for light from a distant object to reach us?

Thus we encounter the essence of the causal horizon. Light from an object 20 billion light-years away could not yet have reached us. This doesn't just state that we can't see it - In any meaningful way, such an object simply does not exist in our universe.

Update to rebut Briglass' argument: I wrote the above explanation from the purely classical perspective. I didn't mention such ideas as inflation, or the possibility of an anisotropic universe, or the EPR paradox of quantum physics, or Robertson-Walker, or even (most of) relativity (other than the idea that nothing can travel faster than the speed of light), because I wrote it for the average reader, rather than for physicists and cosmologists.

I will grant that perhaps the word "perfect" goes a tad too far, but even taking every possible variation on the speed of light (short of it not existing as an upper limit in our universe), the geometry of the universe, and the flatness (or lack thereof) of spacetime into consideration, the core idea remains sound and the actual distances involved would change very little (percentage-wise).
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I do not claim to be a particle physicist, nor do I claim to be a wacky futurist, ok maybe a little. I am simply a concerned citizen of the universe, wary of faults made by our historical cosmologists.

The first red flag that pops up in my mind while reading pla's assertment of the "causal radius" scenario is the phrase "perfect sphere." Remember how Galileo's peers believed the their universe to be a perfect sphere? Well, Galileo then proved, although in quite a posthumous manner, that the planets do not move around the earth in perfect circles. Instead, the path of the planets are irregular.

Taking only that historical experience into account, why should I believe that the universe, a system of great girth and complexity, would ever expand in a uniform shape... a sphere, nonetheless. What about the fact that light is subject to gravity? The light which is supposedly carving out our perfect spherical universe at the speed of itself is also bending around all over the place. As long as a single photon strays from it's original course as a ray from the point of the big bang, the universe is no longer a perfect sphere.

In fact, as Einstein predicted early in the 20th century, scientists have verified that light in fact bends great distances when subject to enough gravitational influence. In 1979, British Astronomers verified theories about the relationship between light and gravity Einstein had put forth in his 1936 essay "Lens-like Action of a Star by the Deviation of Light in the Gravitational Field." Although photons do not have mass, scientists noticed that a large cluster of galaxies between us and a far away quasar was successfully bending the light coming from the quasar. The apparent "binary quasar" was just an optical illusion. Think of all the other large clumps of matter in the universe, and all the light that it is bending.

I'm sure some plastic mind out there is thinking that perhaps the light which is racing at the edge of the universe is out of matter's gravitational reach. But this light came from the same spot as a universal amount of matter. Surely a major amount of this gravitationally induced light-warping came nearer to the birth of the universe than farther.

http://www.scibridge.sdsu.edu/coursemats/introsci/sysinteractions/grav_lenses/

Update:I must say that I meant to argue against the fact that the shape of the matter and light in the universe itself is spherical. What pla refers to in the writeup above is the PROBABLE extremities of the universe, given the maximum distance light could have travelled in all directions since the big bang.

Thanks to Olathe for helping me work through the matter.

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