Testing the spatial geometry of the Universe with TianQin: Prospect of using supermassive black hole binaries

¹ School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, PR China
² Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, PR China
³ Department of Physics, College of Sciences, Northeastern University, Shenyang 110004, PR China
⁴ Department of physics, Chongqing University, 400044 Chongqing, PR China
e-mail: cqujinli1983@cqu.edu.cn
⁵ Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, PR China
e-mail: caoshuo@bnu.edu.cn
⁶ Department of Astronomy, Beijing Normal University, Beijing 100875, PR China
⁷ School of Physics and Astronomy, China West Normal University, Nanchong 637009, PR China
e-mail: qqjiangphys@yeah.net

Received: 25 December 2022
Accepted: 21 October 2023

Abstract

Context. The determination of the spatial geometry of the Universe plays an important role in modern cosmology. Any deviation from the cosmic curvature Ω_K = 0 would have a profound impact on the primordial inflation paradigm and fundamental physics.

Aims. In this paper, we carry out a systematic study of the prospect of measuring the cosmic curvature with the inspiral signal of supermassive black hole binaries (SMBHBs) that could be detected with TianQin.

Methods. The study is based on a method that is independent of cosmological models. It 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 evaluated whether TianQin produced robust constraints on the cosmic curvature parameter Ω_k. More specifically, we considered three-year to ten-year observations of supermassive black hole binaries with total masses ranging from 10³ M_⊙ to 10⁷ M_⊙.

Results. Our results show that in the future, with the synergy of ten-year high-quality observations, we can tightly constrain the curvature parameter at the level of 1σ Ω_k = −0.002 ± 0.061. Moreover, our findings indicate that the total mass of SMBHB does influence the estimation of cosmic curvature, as implied by the analysis performed on different subsamples of gravitational wave data.

Conclusions. Therefore, TianQin is expected to provide a more powerful and competitive probe of the spatial geometry of the Universe, compared to future spaced-based detectors such as DECIGO.