Quantum gravity without gravitons

Charles Choi writes on Scientific American:
In a paper recently accepted by the journal Classical and Quantum Gravity, however, astrophysicist Richard Lieu of the University of Alabama, Huntsville, argues that LIGO should already have detected gravitons if they carry as much energy as some current models of particle physics suggest. It might be that the graviton just packs less energy than expected, but Lieu suggests it might also mean the graviton does not exist.
Loop quantum gravity does not use gravitons as building blocks.

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