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What kind of shape of the universe is being suggested in loop quantum gravity?

From what I know LQG postulates a more or less discrete universe, rather than a continuous one. Does this also mean that it postulates that space is finite? Like, for example in the shape of a doughnut?

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No, the point-wise-connected space lattice in LQG (at least as described by Lee Smolin, one of its inventors) does not close up on itself. I do not know if it is possible for that to be the case; perhaps one of the experts here can weigh in on this aspect of it.

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