There are debates that are still raging about whether or not the cosmogical constant an indeed be positive in string theory. String theory works most naturally if space time is ten mensional, but some versions of it are more than four dimensional. Different geometrically interesting shapes give rise to different low energy laws of physics, including different values of the cosmological constant. And so in thecosmological multi verse, as far as we know, with the kind of calculational techniques we have, there are an infinite number of universes out there,. at least if you include the future, as in the past, as well as the present moment.

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