Universe is expanding at enormous speed I'm not an expert but I've come to understand that the universe is expanding at enormous speed. That means that all of the visible galaxies are moving away from us at great speed. 
I also came to understand that, eventually (in many many years), all the galaxies and all of the rest of the objects outside our own galaxy will move so far away from us that it will be impossible for us to look (or measure) them.
This means that eventually our entire observable universe will be our own galaxy and it will be impossible for us to measure anything else, and scientific measurements at that point in time will not correspond to the actual reality... because data will show that other galaxies don't exist.
But I have two questions regarding this phenomena:


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*How is it that the light won't reach us anymore? Is the expansion happening at greater speed than light itself, making it impossible for it to ever reach anything?

*If scientific measurements, at that point in time, will prove to be wrong, because they will show that galaxies don't exist (while they actually do exist), doesn't that mean that something similar could be happening right now as well? We could be measuring something about the universe that we're dead sure about, but it won't be the actual reality.
 A: I'd like to expand a bit on the answer to the second question, but for completeness I'll do both.


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*As said in JasonR's answer, the expansion of space isn't limit by the speed of light. So objects can be moving at moderate speeds, but because the space between them and us expands faster than light, it's emissions will never reach us. For this reason, there are already regions of space that are beyond our horizon. Whether or not this will always be depends on what "Big Thing" your cosmology ends with. If it's a "Crunch", then everything comes back together in a reverse "Bang" at the end of time. If it's just a "Freeze", then the acceleration expands and possibly even accelerates forever.

*Abraham Loeb wrote a curious paper (available on the arXiv) about how 
to reach cosmological conclusions in the absence of nearby galaxies. About 100 billion years from now, all the galaxies in our Local Group will be beyond the horizon of the Milky Way (or rather Milkomeda, after the Milky Way collides with Andromeda), and the CMB will be at a wavelength longer than the observable Universe. But you'll still be able to reach conclusions about cosmology by using hypervelocity stars being ejected from the galaxy. The point is that you can still get accurate results about the global structure of the Universe using local results.
As for our current model, we have a great deal of evidence that the cosmos is structured according to the Concordance Model. You can always say "it might turn out to be wrong", but it can't turn out to be that wrong because of said evidence. It's like GR as a generalization of Newtonian gravity: yes, Newton was "incorrect" but his theory was also quite accurate, to the extent that we still use it for, say, N-body simulations of star clusters.
A: *

*The expansion of space itself is not limited by the velocity of light.  Even now there are parts of the universe that are receeding from us at a relative velocity greater than that of light (hence why we have observable vs. actual universe terminology).

*We're not really sure what sort of conclusions any far future scientists will draw at such a distant time.  Perhaps the CMB will still give them the clues they need to figure out that the galaxy itself is not the entire universe?  However, it is always possible that we have something totally wrong.  That's the beauty of science, they follow the evidence.  And just because they figure out that something they thought was right is actually wrong, is no excuse to substitute whatever harebrained idea in place of what the evidence supports (religions, mystics, Deepak Chopra, etc. are notorious for that sort of BS).
A: Might as well post it here too.
From a very amateur standpoint:


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*Pretty sure that light will still reach us, it'll just take a ridiculous amount of years to hit us (dwarfing 13 billion years at the farthest observed galaxy). I know that right after the big bang, Stephen Hawking claims the universe expanded many light years in a matter of minutes. However, while the universe may expand at faster than the speed of light, matter cannot. Also, as things drift apart, some astronomers and physicists think we're in for a "big crunch." The example you're giving is more consistent with Hawking's views on a "big chill;" where everything eventually gets so far apart we cannot reach another source of warmth with our fuel supply once everything burns up and is "recycled" enough times. This leaves only black holes, neutron stars, and other non-energy/very limited energy emitting phenomena within our reach.

*Can't say that scientific measurements would automatically be wrong if we already have a database of today's current data for future scientists to work from. Evidence of galaxies will still remain, because we will still be a part of our own galaxy. Galaxies are spreading far apart from each other (in almost all cases, ours is an exception as it's destined to collide with the Andromeda galaxy), but the matter in the galaxy will continue to orbit the center of mass (a super massive black hole). 
We're also already measuring stuff we're "dead sure" about in a public perspective, but not in a scientific one. Early models saying the Earth was the center of the solar system were actually more mathematically accurate than the later developed Sun centered model. Eventually further advances proved the Sun model was correct, and the math then followed. Same thing exists today. Until general relativity and quantum mechanics can be mathematically linked, one or both will need to be replaced by a future model that might already exist, but not make mathematical sense quite yet.
