Parameter estimation of eccentric gravitational waves with a decihertz observatory and its cosmological implications

Eccentricity of compact binaries can improve the parameter estimation of gravitational waves (GWs). In this paper, we first investigate the parameter estimation of eccentric GWs with decihertz observatory. We consider two scenarios for the configuration of DECIGO, i.e., the one cluster of DECIGO with its design sensitivity and B-DECIGO which also has one cluster but with inferior sensitivity as a comparison. We adopt the Fisher matrix to estimate the parameter errors. By mocking up the typical binaries in GWTC-3, we find a nonvanishing eccentricity can significantly improve the estimation for almost all waveform parameters. In particular, the localization of typical binary black holes (BBH) can achieve $\mathcal{O}(10-10^{3.5})$ factors of improvement when the initial eccentricity $e_0=0.4$ at 0.1 Hz. The precise localization of binary neutron stars (BNS) and neutron star--black hole binaries (NSBH), together with the large improvement of localization of BBH from eccentricity in the mid-band, inspire us to construct the catalogs of golden dark sirens whose host galaxies can be uniquely identified. We find that with only one cluster of DECIGO running 1 year in its design sensitivity, hundreds of golden dark BNS, NSBH, and tens of golden dark BBH can be observed. Eccentricity can greatly increase the population of golden dark BBH from $\sim 7~(e_0=0)$ to $\sim 65~(e_0=0.2)$. Such an increase of population of golden dark BBH events can improve the precision of Hubble constant measurement from 2.06\% to 0.68\%, matter density parameter from 64\% to 16\% in $\Lambda$CDM model. Through the phenomenological parameterization of GW propagation, the constraints of modified gravity can be improved from 6.2\% to 1.6\%. Our results show the remarkable significance of eccentricity for the detection and parameter estimation of GW events, allowing us to probe the Universe precisely.