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A violent explosion picked up by a NASA satellite earlier this year is the oldest object ever seen by astronomers, its light having been emitted some 13 billion years ago. At that time the universe was roughly 5 percent of its present age and the big bang was a fairly recent occurrence, having taken place just 600 million years earlier.
So why would that light arrive after 13 billion years rather than, say, two billion years in a much smaller universe, passing the point in space that would eventually hold us?
Spacetime is highly curved at cosmological scales, and as a result the expansion of the universe is inherently general relativistic; it cannot be understood with special relativity alone.
Now, the ant IS moving faster than the rubber band is getting longer, so it WILL eventually get to the other end. But what started out looking like would be about a foot of travel-time has turned into twenty feet by the time the ant gets to the other end. So when the ant turns around to see where it started from, it suddenly looks like TWENTY feet! And, where it started out looking like a five-minute trip, because there kept being more and more and more distance, it turned out to be twenty minutes.