Anisotropy of the gravitational-wave standard sirens and its cosmological applications

Abstract We analyze the anisotropic factors present in the gravitational wave signal, such as the peculiar velocity of the observer and the inhomogeneous distribution of matter in the universe. We model the gravitational wave source as a standard siren, extract the anisotropic part of its luminosity distance $$d_L$$ d L , and obtain the Hubble parameter H(z) by direct calculation instead of integration. Finally, we derive the equation of state $$w_\mathrm{DE}(z)$$ w DE ( z ) for the dark energy by both model-dependent and model-independent methods, and further investigate the cosmological significance of the simulated H(z) measurements. The advantage of this approach is that it makes full use of the anisotropic part of the $$d_L$$ d L data, which directly gives the value of H(z) at certain redshifts. This approach is sensitive to the local features of H(z) and does not depend on the cosmological model.