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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 beenextensively used to perform this test. The results obtained so far suggested atension between observations and predictions of the $\Lambda$CDM model.However, the dataset of $H(z)$ direct measurements from cosmic chronometers andBAO was quite limited. This motivated us to study the performance of this teston a larger sample obtained in an alternative way. In this Letter, we proposethat gravitational wave (GW) standard sirens could provide large samples of$H(z)$ measurements in the redshift range of $0<z<5$, based on the measurementsof dipole anisotropy of luminosity distance arising from the matterinhomogeneities of large-scale structure and the local motion of observer. Wediscuss the effectiveness of our method in the context of the future generationspace-borne DECi-herz Interferometer Gravitaional-wave Observatory (DECIGO),based on a comprehensive $H(z)$ simulated data set from binary neutron starmerger 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 thebest description of our Universe. We also discuss the potential of ourmethodology in determining possible evidence for dark energy evolution,focusing on its performance on the constant and redshift-dependent dark energyequation of state.

Distinguishing $\Lambda$CDM from evolving dark energy with the future gravitational-wave space-borne detector DECIGO