There is good reason to suppose that the Universe has more than three spatial dimensions. The first dedicated search for warped extra dimensions has drawn a blank, but hopes are high for the future.
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Allanach, B. Do the space-warp. Nature Phys 1, 15–16 (2005). https://doi.org/10.1038/nphys130
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DOI: https://doi.org/10.1038/nphys130