Distinguishing ΛCDM from Evolving Dark Energy with Om Two-point Statistics: Implications from the Space-borne Gravitational-wave Detector

The Omh ^2 ( z _i , z _j ) two-point diagnostics was proposed as a litmus test of the ΛCDM model, and measurements of the cosmic expansion rate H ( z ) have been extensively used to perform this test. The results obtained so far suggested a tension between observations and predictions of the ΛCDM model. However, the data set of H ( z ) direct measurements from cosmic chronometers and baryon acoustic oscillations was quite limited. This motivated us to study the performance of this test on a larger sample obtained in an alternative way. In this paper, we propose that gravitational-wave (GW) standard sirens could provide large samples of H ( z ) measurements in the redshift range of 0 < z < 5, based on the measurements of the dipole anisotropy of luminosity distance arising from the matter inhomogeneities of the large-scale structure and the local motion of the observer. We discuss the effectiveness of our method in the context of the space-borne DECi-herz Interferometer Gravitational-wave Observatory, based on a comprehensive H ( z ) simulated data set from binary neutron star merger systems. Our results indicate that in the GW domain, the Omh ^2 ( z _i , z _j ) two-point diagnostics could effectively distinguish whether ΛCDM is the best description of our Universe. We also discuss the potential of our methodology in determining possible evidence for dark energy evolution, focusing on its performance on the constant and redshift-dependent dark energy equation of state.