Impacts of gravitational-wave standard siren observation of the Einstein Telescope on weighing neutrinos in cosmology

We investigate the impacts of the gravitational-wave (GW) standard siren observation of the Einstein Telescope (ET) on constraining the total neutrino mass. We simulate 1000 GW events that would be observed by the ET in its 10-year observation by taking the standard ΛCDM cosmology as a fiducial model. We combine the simulated GW data with other cosmological observations including cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and type Ia supernovae (SN). We consider three mass hierarchy cases for the neutrino mass, i.e., normal hierarchy (NH), inverted hierarchy (IH), and degenerate hierarchy (DH). Using Planck+BAO+SN, we obtain ∑mν<0.175 eV for the NH case, ∑mν<0.200 eV for the IH case, and ∑mν<0.136 eV for the DH case. After considering the GW data, i.e., using Planck+BAO+SN+GW, the constraint results become ∑mν<0.151 eV for the NH case, ∑mν<0.185 eV for the IH case, and ∑mν<0.122 eV for the DH case. We find that the GW data can help reduce the upper limits of ∑mν by 13.7%, 7.5%, and 10.3% for the NH, IH, and DH cases, respectively. In addition, we find that the GW data can also help break the degeneracies between ∑mν and other parameters. We show that the GW data of the ET could greatly improve the constraint accuracies of cosmological parameters.