>> that shortly after the detector came online we just happened to observe the exact moment a billion years ago that two black holes collided?
Counterintuitive, but yes. Because it happened billions of years ago, it happened a long long way away. The sphere of objects billions of years away/ago is far larger than those closer to us. So such a detector should be detecting exponentially more very old objects than new ones. Given the rarity, I would expect nearly all detected events to have happened long long ago in galaxies far far away.
Also, models point to such events being more common in the distant past where there were more black holes (primordials) floating around than there are now.
If one event happens 1B years ago 1B light years away and another event happens at .5B years ago .5B light years away... how would we know there are two events?
The wave may contain the information necessary to describe the event that created it. If you know, perhaps by frequency, that the wave came from two super-massive black holes spinning around each other at a given rate, then you know how massive each hole should be. From that you can predict the energy of the wave. And from that you know how far away the event must be for the energy behind the wave to have spread so thin. It's basically the same process as calculating distance via cepheid variable stars.
Counterintuitive, but yes. Because it happened billions of years ago, it happened a long long way away. The sphere of objects billions of years away/ago is far larger than those closer to us. So such a detector should be detecting exponentially more very old objects than new ones. Given the rarity, I would expect nearly all detected events to have happened long long ago in galaxies far far away.
Also, models point to such events being more common in the distant past where there were more black holes (primordials) floating around than there are now.