2022ApJ...930..122C

Extreme-mass-ratio inspirals (EMRIs) are important targets for future space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA). Recent works suggest that EMRIs may reside in a population of newly discovered X-ray transients called "quasiperiodic eruptions" (QPEs). Here, we follow this scenario and investigate whether LISA could in the future detect the QPEs. We consider two specific models, in which the QPEs are made of either stellar-mass objects moving on circular orbits around massive black holes (MBHs) or white dwarfs (WDs) on eccentric orbits around MBHs. We find that in either case the five QPEs detected so far are too weak to be resolvable by LISA. However, if QPEs are made of eccentric WD-MBH binaries, they radiate GWs over a wide range of frequencies. The broad spectra overlap to form a background that peaks in the milli-Hertz band and has a signal-to-noise ratio of 9-17 even in the most pessimistic scenario. The presence of this GW background in the LISA band could impact future searches for seed black holes at high redshift as well as stellar-mass binary black holes in the local universe.