There is no single approach to the quantization of gravity. Rather, multiple models are based on various assumptions, and experimental tests of Planck-scale physics present a particular challenge.
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Mattingly, D. Quantum gravity: Searching in the dark. Nat Astron 1, 0159 (2017). https://doi.org/10.1038/s41550-017-0159
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DOI: https://doi.org/10.1038/s41550-017-0159