Improving the Cosmological Constraints by Inferring the Formation Channel of Extreme-mass-ratio Inspirals

Extreme-mass ratio inspirals (EMRIs) could be detected by space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA), TianQin and Taiji. In general, locating EMRIs by space-borne GW detectors can help us select the candidate host galaxies which can be used to infer the cosmic expansion history. In this paper, we show that the localization information of EMRIs can also be used to select the candidate host AGNs which can be used to infer the formation channel of the EMRIs and extract more precisely the redshift probability distributions of the EMRIs. Using the EMRIs that are expected to be detected by TianQin and LISA and the galaxy catalog that can be provided by the Chinese Space Station Telescope for the analysis, we find that TianQin can constrain the Hubble-Lemaître constant H_0 to a precision of about 3%-8% and the dark energy equation of state parameter w_0 to about 10%-40%, the network composed of TianQin and LISA can improve the precisions of H_0 and w_0 to about 0.4% - 7% and 4%-20%, respectively, without considering the effects of AGNs. Furthermore, combining the detected EMRIs with AGN catalog by the statistical framework of likelihood-ratio-based, we find TianQin can establish the EMRI-AGN correlation with about 500 EMRIs if all of the EMRIs indeed originate in AGNs, and the TianQin+LISA network can reduce this required number to about 30. Once the EMRI-AGN correlation is confirmed, the combination of the EMRIs and AGN catalog can significantly improve the constraints on the cosmological parameters. These results demonstrate the potentials of using EMRIs as well as galaxy and AGN catalogs to constrain the cosmological parameters and astrophysical models.