Imprints of quantum gravity effects on gravitational waves: a comparative study using extreme mass-ratio inspirals

Within a generally covariant Hamiltonian framework of loop quantum gravity (LQG), two black hole models parameterized by a quantum correction $\zeta$ have recently been constructed. Using extreme mass-ratio inspirals (EMRIs) as high-precision probes, we investigate the imprints of this LQG deformation in the surrounding spacetime. Waveforms generated via an improved augmented analytic kludge (AAK) model in both LQG black hole backgrounds and in Schwarzschild spacetime are compared through a faithfulness analysis. This allows us to quantify the detectability of the deviation with LISA and to derive constraints on $\zeta$ based on a detection threshold. We find that the first LQG black hole model produces significantly stronger signatures in EMRI signals than the second, making its quantum gravity effects more accessible to future space-borne gravitational-wave detection.