I received an email asking this question: "Do you know of any physical evidence or proof that indicates other universes exist?" With the growing popularity of multiverse explanations, one might expect to see a relatively large body of evidence supporting the idea. In reality only a handful of observations directly impact multiverse models and those measurements tend to argue against the existence of "other universes."
Virtually all the physical evidence addressing the multiverse arises from studies of the cosmic microwave background (CMB) radiation. I discussed how astronomers used this radiation to extract cosmological parameters in a previous TNRTB.
All inflationary models that produce a Level II multiverse (and a spatially infinite Level I multiverse) lead to an open geometry for our observable universe (look here for definitions). This means that Ωk, the curvature of the universe, should measure positive. However, the best measurement of this Ωk quantity is negative, although the error bars include some positive value. The measured values reported by Eiichiro Komatsu and colleagues are -0.0170 < Ωk < 0.0068 (see table 2). If Ωk ends up measuring less than zero, no inflation-generated Level II multiverse exists.
Based on the small measured power in the low-order multipoles of the CMB spectrum, some have argued that the universe is comparable in size to the observable universe. While these models require a more complex topology for the universe than normally assumed, if future CMB measurements confirm their predictions, they would rule out any form of a Level I multiverse.
Two recent measurements seem to validate the idea that a large Level I multiverse (at least one thousand times the size of the observable universe) exists. As with the evidence described above, both measurements involved analysis of the CMB radiation. One paper argues that the observable universe is moving in a particular direction. This would require a pre-inflationary gravitational tug from a region of space that moved far beyond the observational horizon during the inflationary epoch. The other paper indicates the CMB exhibits an asymmetry that is best explained in the context of a vast region of space beyond the observable horizon.
As you can see, only a sparse amount of physical evidence weighs in on the existence of any Level I or Level II multiverse. Additionally, the available evidence only weakly argues for or against the multiverse. Fortunately, more sensitive missions are planned, which will provide greater clarity that, in turn, stand to validate or invalidate cosmic creation models. Exciting times lay ahead in multiverse research.
If you would like to see a question about the multiverse addressed in this forum, send it to firstname.lastname@example.org.