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Although the spatial curvature has been precisely determined via the cosmic microwave background (CMB) observation by Planck satellite, it still suffers from the well-known cosmic curvature tension. As a standard siren, gravitational waves (GWs) from binary neutron star mergers provide a direct way to measure the luminosity distance. In addition, the accelerating expansion of the universe may cause an additional phase shift in the gravitational waveform, which allows us to measure the acceleration parameter. This measurement provides an important opportunity to determine the curvature parameter $\Omega_k$ in the GW domain based on the combination of two different observables for the same objects at high redshifts. In this study, we investigate how such an idea could be implemented with future generation of space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO) in the framework of two model-independent methods. Our results show that DECIGO could provide a reliable and stringent constraint on the cosmic curvature at a precision of $\Delta\Omega_k$=0.12, which is comparable to existing results based on different electromagnetic data. Our constraints are more stringent than the traditional electromagnetic method from the Pantheon SNe Ia sample, which shows no evidence for the deviation from the flat universe at $z\sim 2.3$. More importantly, with our model-independent method, such a second-generation space-based GW detector would also be able to explore the possible evolution $\Omega_k$ with redshifts, through direct measurements of cosmic curvature at different redshifts ($z\sim 5$). Such a model-independent $\Omega_k$ reconstruction to the distance past can become a milestone in gravitational-wave cosmology., Comment: 10 pages, 6 figures, accepted for publication in ApJ

In this paper, we use a newly compiled sample of ultra-compact structure in radio quasars and strong gravitational lensing systems with quasars acting as background sources to constrain six spatially flat and non-flat cosmological models ($\Lambda$CDM, PEDE and DGP). These two sets of quasar data (the time-delay measurements of six strong lensing systems and 120 intermediate-luminosity quasars calibrated as standard rulers) could break the degeneracy between cosmological parameters ($H_0$, $\Omega_m$ and $\Omega_k$) and therefore provide more stringent cosmological constraints for the six cosmological models we study. A joint analysis of the quasar sample provides model-independent estimations of the Hubble constant $H_0$, which is strongly consistent with that derived from the local distance ladder by SH0ES collaboration in the $\Lambda$CDM and PEDE model. However, in the framework of a DGP cosmology (especially for the flat universe), the measured Hubble constant is in good agreement with that derived from the the recent Planck 2018 results. In addition, our results show that zero spatial curvature is supported by the current lensed and unlensed quasar observations and there is no significant deviation from a flat universe. For most of cosmological model we study (the flat $\Lambda$CDM, non-flat $\Lambda$CDM, flat PEDE, and non-flat PEDE models), the derived matter density parameter is completely consistent with $\Omega_m\sim 0.30$ in all the data sets, as expected by the latest cosmological observations. Finally, according to the the statistical criteria DIC, although the joint constraints provide substantial observational support to the flat PEDE model, they do not rule out dark energy being a cosmological constant and non-flat spatial hypersurfaces., Comment: 11 pages, 5 figures, accepted for publication in A&A

In this paper, we analyze the implications of the latest cosmological data sets to test the Etherington distance duality relation (DDR), which connects the luminosity distance ${D}_{L}$ and angular diameter distance ${D}_{A}$ at the same redshift. For ${D}_{L}$, we consider the simulated data of gravitational waves from the third-generation gravitational wave detector [the Einstein Telescope (ET)], which can be considered as standard candles (or standard siren), while the angular diameter distances ${D}_{A}$ are derived from the newly compiled sample of compact radio quasars observed by very-long-baseline interferometry (VLBI), which represents a new type of cosmological standard ruler. Alleviating the absorbtion and scattering effects of dust in the Universe, this will create a valuable opportunity to directly test DDR at much higher precision with the combination of gravitational wave (GW) and electromagnetic (EM) signals. Our results show that, with the combination of the current radio quasar observations, the duality-distance relation can be verified at the precision of ${10}^{\ensuremath{-}2}$. Moreover, the Einstein Telescope would produce more robust constraints on the validity of such distance duality relation (at the precision of ${10}^{\ensuremath{-}3}$), with a larger sample of compact milliarcsecond radio quasars detected in future VLBI surveys.