The Big Bang Theory concerns the expansion of the universe. In this sense, it obviously makes no sense to ask “where did it happen”, because it literally was happening everywhere.
The confusion comes when you start discussing the Big Bang **singularity**. The introduction of this concept starts causing people to think that there’s a single point in space from which all space was birthed and they make outrageous claims like “the Big Bang is the result of a white hole” which from our previous statements is fancifully incorrect. The singularity results from rewinding the clock all the way to t=0 that the totality of space is now infinitely dense. The important word here is **totality** of space. Again, not a singular point. Everywhere. It’s a description of the universe in that “point of cosmological time”.
It’s very important to understand that the Big Bang singularity is **not a component of the existing standard model**. In fact the singularity is itself not even existing in spacetime. There’s a reason you’re talking about it, though. It’s popular. People think of it as the “when time started” because of the way the mathematics works out, but it’s non-mathematical thinking. Time doesn’t need to “start”, it’s purely an index, a coordinate for ordering things. Same thing with the singularity purely capturing a mathematical statement on limits. All inflationary models currently don’t make any statement on what happens before the “Planck Time” so anyone attempting to do so is purely doing a thought experiment. If they attempt to pass it as what the real physical model tells us, then they are admitting ignorance.
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