What exactly do astrophysicists mean when they say that the universe is expanding at an accelerated rate? Assuming that the universe is a sphere, do they mean that the radius of the universe increases exponentially, or do they mean that the volume of the universe increases exponentially? Or is it that the universe is not a sphere at all, in that case, what shape is it then? Or does it even have a shape?
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Qmechanic
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If it is a sphere and the radius increases exponentially, then so does its volume... We don't know the global topology of the universe. It could be closed and curved (unlikely because the universe is incredibly flat), or it could be closed and flat such as a torus. It could be open and curved (once again unlikely), or open and flat. But we do know what topology it can't be. Namely, every topology having a non-vanishing first or second Stiefel-Whitney class is impossible. – Jeanbaptiste Roux May 04 '23 at 14:39
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1Does this answer your question? Big Bang: what is it exactly that is expanding? and What does it mean by universe is expanding? I know that the universe is expanding because spacetime is expanding but again what does it mean? – Quillo May 04 '23 at 14:46
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1See also Did the Big Bang happen at a point? for more on what the Big Bang actually was, and How does the Hubble parameter change with the age of the universe? for how to calculate the expansion. – John Rennie May 04 '23 at 14:59