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The Big Bang Observer is a proposed spacecraft to study gravitational waves. Especially the one that are thought to originate from the Big Bang. Question. How can we observe waves that has an origin at the beginning of time? Doesn't it implies then that we were there when it happened so that the wave were created and then travelled to us?

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The aim of the Big Bang Observer would be to study gravitational waves generated during the inflationary period that took place some $10^{-32}$ seconds after the Big Bang.

One of the frequently misunderstood aspects of the Big Bang is that it didn't happen at some point, with the universe expanding outwards from that point, but instead happened everywhere in space. This is discussed in Did the Big Bang happen at a point? This means if you pick any random point in the universe the Big Bang happened at that point (as well as everywhere else) some 13.7 billion years ago. So if that point happens to be 13.7 billion light years away at present time the gravitational waves generated during inflation 13.7 billion years ago are reaching us right now.

This is what is meant by observing the Big Bang. We would be literally observing the gravitational waves that were generated $10^{-32}$ seconds after the Bang Bang and have spent the time since then travelling towards us.

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