Distinguishing ΛCDM from evolving dark energy with the future gravitational-wave space-borne detector DECIGO

The $Omh^2(z_i,z_j)$ two point diagnostics was proposed as a litmus test of $\Lambda$CDM model and measurements of 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 $\Lambda$CDM model. However, the dataset of $H(z)$ direct measurements from cosmic chronometers and BAO was quite limited. This motivated us to study the performance of this test on a larger sample obtained in an alternative way. In this Letter, 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 dipole anisotropy of luminosity distance arising from the matter inhomogeneities of large-scale structure and the local motion of observer. We discuss the effectiveness of our method in the context of the future generation space-borne DECi-herz Interferometer Gravitaional-wave Observatory (DECIGO), based on a comprehensive $H(z)$ simulated data set from binary neutron star merger systems. Our result indicate that in the GW domain, the $Omh^2(z_i,z_j)$ two point diagnostics could effectively distinguish whether $\Lambda$CDM 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.