By studying quantum cosmology I was asking myself if the fact that the universe is expanding, so space is expanding and with it I would say that phase space is also expanding, so it's a non-unitary evolution, am I right? If yes, can unitarity be restored in a multiverse picture? Because I am always troubled when I hear that as we have experimentally verified the unitarity of low energy QM, by pushing further we arrive at the concluse that the multiverse can be extended from $t= - \infty$ to $t= + \infty$, sounds a bit dogmatic to me.
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