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I understand that it is possible to detect the most distant objects in space over 13 billion light years away from us and that the universe is 13.75 billion years old.

Does this imply that there were some objects many billions of light years away from us even in the earliest stages of the expansion of the universe, has the universe at some point expanded faster than the speed of light or is my mental image of the expansion process incorrect?

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I think this could use just a little bit more elaboration on what your mental image is. How do you conclude there were distant objects, or that superluminal expansion is needed? I can see some ways to interpret what you are asking, but I don't want to put words in your mouth. –  Chris White Jan 12 '13 at 22:06
    
Ok - I'll try to do it without getting in a muddle! If the light has taken 13bn years to travel to us, it started its journey 13bn years ago. But assuming expansion at light speed, we were only 0.75bn light years away from that object when the light started its journey to us. So how has the light taken 13bn years to reach us? –  AJ. Jan 12 '13 at 22:22
    
Apologies for the incorrect assumption. Re-thinking this from your comment, of course the expansion would not have to be super luminal - it would simply have to be close to that of light speed. Is that correct? –  AJ. Jan 12 '13 at 22:24
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Yes, assuming it was constant. You may want to take a look at physics.stackexchange.com/questions/48041/… –  Chris White Jan 12 '13 at 22:42
    
Excellent link - thank you. –  AJ. Jan 12 '13 at 22:58

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The link that Chris gave is a good answer, but there are a couple of related issues to mention:

Firstly you ask:

has the universe at some point expanded faster than the speed of light

and the answer is that, yes, it has (or at least we think so), and this expansion is called inflation. Secondly you ask:

Does this imply that there were some objects many billions of light years away from us even in the earliest stages of the expansion of the universe

and the answer is again yes (or at least we think so). The Big Bang wasn't an expansion from a point. If you take the simplest model of the universe, the FLRW metric, then if the universe is infinite now it has always been infinite right back to the Big Bang. There are loads of answers related to this point on this site. See for example my recent answer to Was the singularity at Big Bang perfectly uniform and if so, why did the universe lose its uniformity? or just search the site for FLRW metric.

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In fact, most of even the observable Universe is at present time moving away from us faster than light. A large part of them were already moving away from us faster than light when the light we currently receive from them was emitted. What makes inflation special isn't that it was superluminal, but that it was exponential. –  Thriveth Jun 6 '13 at 15:27

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