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It's important to physicists, because physicists want a consistent (without logical contradictions) understanding of how the universe works.

As far as everyday practical applications, cosmology and quantum gravity will have little impact. Cosmology is the study of the large-scale structure of the universe, which we probably won't be physically exploring in our lifetimes, and quantum gravity is only relevant at energies so high that we will probably need to build machines exceeding the size of the Earth to make good use of it.

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