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We explore the prospects for constraining cosmology using gravitational-wave(GW) observations of neutron-star binaries by the proposed Einstein Telescope(ET), exploiting the narrowness of the neutron-star mass function. Doubleneutron-star (DNS) binaries are expected to be one of the first sourcesdetected after "first-light" of Advanced LIGO and are expected to be detectedat a rate of a few tens per year in the advanced era. However the proposed ETcould catalog tens of thousands per year. Combining the measured sourceredshift distributions with GW-network distance determinations will permit notonly the precision measurement of background cosmological parameters, but willprovide an insight into the astrophysical properties of these DNS systems. Ofparticular interest will be to probe the distribution of delay times betweenDNS-binary creation and subsequent merger, as well as the evolution of thestar-formation rate density within ET's detection horizon. Keeping H_0,\Omega_{m,0} and \Omega_{\Lambda,0} fixed and investigating the precision withwhich the dark-energy equation-of-state parameters could be recovered, we foundthat with 10^5 detected DNS binaries we could constrain these parameters to anaccuracy similar to forecasted constraints from future CMB+BAO+SNIameasurements. Furthermore, modeling the merger delay-time distribution as apower-law, and the star-formation rate (SFR) density as a parametrized versionof the Porciani and Madau SF2 model, we find that the associated astrophysicalparameters are constrained to within ~ 10%. All parameter precisions scaled as1/sqrt(N), where N is the number of cataloged detections. We also investigatedhow precisions varied with the intrinsic underlying properties of the Universeand with the distance reach of the network (which may be affected by thelow-frequency cutoff of the detector).

Cosmology with the lights off: Standard sirens in the Einstein Telescope era