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In this work, using the Gaussian process, we explore the potentiality of future gravitational wave (GW) measurement to probe cosmic opacity through comparing its opacity-free luminosity distance (LD) with the opacity-dependent one from type Ia supernovae (SNIa). GW data points are simulated from the third-generation Einstein Telescope, and SNIa data are taken from the Joint Light Analysis (JLA) or Pantheon compilation. The advantages of using the Gaussian process are that one may match SNIa data with GW data at the same redshift and use all available data to probe cosmic opacity. We obtain that the error bar of the constraint on cosmic opacity can be reduced to σε∼0.011 and 0.006 at 1σ confidence level (CL) for JLA and Pantheon, respectively, in a cosmological-independent way. Thus, the future GW measurements can give competitive results on the cosmic opacity test. Furthermore, we propose a method to probe the spatial homogeneity of the cosmic transparency through comparing the reconstructed LD from the mock GW with the reconstructed one from SNIa data in a flat ΛCDM with the Gaussian process. The result shows that a transparent universe is favored at 1σ CL, although the best-fit value of cosmic opacity is redshift dependent. [ABSTRACT FROM AUTHOR]

A validation of the cosmic distance-duality relation (CDDR) is crucial because any observational departure from it could be a signal of new physics. In this work, we explore the potentialities of luminosity distance data from the gravitational wave (GW) standard sirens of the future Einstein Telescope (ET) to test the CDDR. The angular diameter distance data are used from the galaxy cluster samples and the baryon acoustic oscillation (BAO) measurements. The basic advantage of GW measurement substituting for the observation from the type Ia supernovae (SNIa) is that the luminosity distance from GW is insensitive to the nonconservation of the number of photons. By simulating 550 and 1000 data points of future GW measurements in the low redshift range 0