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In a documentary written in collaboration with Stephen Hawking, the narrator (supposedly Stephen Hawkings) says that by the time the cosmos was 10 minutes old, it had already expanded thousands of light years in diameter. How is it possible that matter was traveling faster than light?

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The metric expansion of space is a fundamentally different phenomenon than the relative motion of two objects in the flat spacetime of Special Relativity:

While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, it places no theoretical constraint on changes to the scale of space itself. It is thus possible for two objects to be stationary or moving at speeds below that of light, and yet to become separated in space by more than the distance light could have travelled,

Also, see this question and the accepted answer.

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In fact, the accepted answer is not as thorough or accurate as the one given by "Pulsar" below it (which also has more upvotes). One problem about the accepted answer is that it equates the Cosmic Event Horizon with the Hubble Sphere, which is only true for a pure, empty De Sitter space, but not generally true. –  Thriveth Jan 14 at 11:18
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Because space itself was expanding faster than the speed of light.

Which is perfectly acceptable by the way with Special Relativity, because the speed of light is only a barrier for matter traveling through space. There is no such limit for the speed with which space itself can expand (or contract), as far as I know.

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