Cosmological implications of two mock TianQin standard siren catalogs generated under different background cosmological models

Abstract: Space-borne gravitational wave (GW) detectors such as TianQin are expected to detect GW standard sirens for cosmological parameter estimation. All previous studies of TianQin adopted the $Λ$CDM model to generate mock standard siren data. In this work, we quantitatively investigate how the choice of background cosmological model affects mock TianQin standard siren (TQSS) catalogs and the corresponding cosmological implications. Adopting the $Λ$CDM model and a redshift-binned dark energy (DE) reconstruction model (the wbin model), we consider the bright standard sirens from massive black hole binary mergers and generate two mock TQSS catalogs, i.e. TQSS1 and TQSS2, respectively. We investigate the difference of the catalogs and further explore their cosmological implications within the Chevallier-Polarski-Linder (CPL) model, both individually and in combination with DESI DR2 baryon acoustic oscillation (BAO) data, $\textit{Planck}$ 2018 cosmic microwave background (CMB) data, and DESY5 type Ia supernova (SN Ia) data. We find that there are only small differences between TQSS1 and TQSS2 catalogs, with a maximum relative difference of $1.48\%$ in the distance-redshift relation. In addition, either the TQSS1 or TQSS2 catalog alone gives cosmological constraints similar to those obtained from SN data, implying that these two catalogs can serve as a complement to mainstream cosmological observations. Most importantly, we find that both TQSS1+DESI DR2+CMB+DESY5 and TQSS2+DESI DR2+CMB+DESY5 are still expected to favor dynamical DE, with these two combinations showing a preference for dynamical DE at $2.3σ$ and $3.8σ$, respectively. Adopting different massive black hole seed models does not impact the cosmological implications of the mock TQSS catalogs. Our study indicates the importance of considering different cosmological models in the standard siren forecasts for DE.