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| | Is The Universe Closed? |
 | | This metric, with k = +1 and R(t) = constant, was the basis of Einstein's 1917 paper, and it was subsequently studied by Alexander Friedmann in 1922 with both possible signs of k and with variable R(t). |
 | | Friedmann realized that this error invalidated Einstein's argument against the possibility of a dynamic universe, and indeed under the condition that the quantity in question vanishes, it is possible to satisfy the field equations with a dynamic model, i.e., with a model of the form given by the Robertson-Walker metric with R(t) variable. |
 | | Of course, at this stage Einstein was assuming a zero cosmological constant, so it may not have occurred to him that it might someday be possible to determine empirically that the expansion of the universe is accelerating, thereby automatically proving that the universe is open. |
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