Probing Quantum Gravity effects with Extreme Mass Ratio Inspirals around Rotating Hayward Black Holes

We investigate extreme mass-ratio inspirals (EMRIs) around a rotating Hayward black hole to assess the detectability of signatures arising from quantum gravity.The quantum parameter ${\alpha }_0$, which encodes deviations from general relativity (GR), introduces extra correction terms in both the orbital frequency and the fluxes. Our results show that after one year of accumulated observation, these corrections induce a detectable dephasing in the EMRI waveform. Using the modified orbital evolution driven by ${\alpha }_0$, we generate waveforms via the augmented analytic kludge (AAK) model implemented in the $\mathtt{\text{FastEMRIWaveforms}}$ package. Furthermore, we utilize the time-delay interferometry (TDI) to suppress the laser noise and phase fluctuations induced by spacecraft motion, and then employ the Fisher information matrix (FIM) to test the sensitivity of LISA in detecting deviations from GR. Our results demonstrate the potential of LISA to probe quantum-gravity effects through high-precision observations of EMRIs.