>>11190505okay, first of all, what "flat" means in this context has nothing to do with it being 2 dimensional. what it means is basically:
>the universe has a close-to-zero curvature on relevant scalesa counterexample to close-to-zero curvature would be if you took a ride on a space ship in outer space, and after 1 lightyear you turned right 60 degrees, and then after another lightyear you turned right another 60 degrees, and then after one year you end up far away from where you started. in flat space you would have traced out a euclidean equilateral triangle and ended up where you started. if you ended up far away from where you started then space wouldn't be flat. that isn't the case to a high degree of accuracy and therefore space is flat.
this doesn't have all that much to do with inflation at first glance. however, if you think deeply about the big bang, then you'd conclude that when the universe was extremely small, like quantum-physics scale small, there would be big fluctuations in the energy density between different parts of the universe we see now. in other words, a quantum-sized universe would have very dense regions and very sparse regions thanks to quantum fluctuations. this would in turn mean (due to general relativity) that certain regions of space would be very positively curved (like a sphere) or very negatively curved (like a saddle-shape).
this would imply that the universe we see is not overall approximately "flat" everywhere we look, but very "bumpy". so in order to explain this, there needs to be a mechanism to smooth over these bumps so that things look flat all over.
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