Testing the spatial geometry of the universe with TianQin: the prospect of using supermassive black hole binaries

Abstract: The determination of the spatial geometry of the universe plays an important role in modern cosmology. Any deviation from the cosmic curvature $\Omega_K=0$ would have a profound impact on the primordial inflation paradigm and fundamental physics. In this paper, we carry out a systematic study of the prospect of measuring cosmic curvature with the inspiral signal of supermassive black hole binaries (SMBHBs) that could be detected with TianQin. The study is based on a cosmological-model-independent method that extended the application of gravitational wave (GW) standard sirens in cosmology. By comparing the distances from future simulated GW events and simulated $H(z)$ data, we evaluate if TianQin would produce robust constraints on the cosmic curvature parameter $\Omega_{k}$. More specifically, we consider 3-yr to 10-yr observations of supermassive black hole binaries with total masses ranging from $10^{3}M_\odot$ to $10^{7}M_\odot$. Our results show that in the future, with the synergy of 10-yr high-quality observations, we can tightly constrain the curvature parameter at the level of $1\sigma$ $\Omega_k=-0.002\pm0.061$. Moreover, our findings indicate that the total mass of SMBHB does influence the estimation of cosmic curvature, implied by the analysis performed on different subsamples of gravitational wave data. Therefore, TianQin is expected to provide a powerful and competitive probe of the spatial geometry of the universe, compared to future spaced-based detectors such as DECIGO.