http://arxiv.org/abs/1707.04152
In this work, we discuss the possibility of using strongly lensed gravitational waves (GWs) and their electromagnetic (EM) counterparts as powerful cosmic rulers. In the EM domain, it has been suggested that the joint observations of the time delay ($\Delta\tau$) between lensed quasar images and the velocity dispersion ($\sigma$) of the lensing galaxy (i.e., the combination $\Delta\tau/\sigma^{2}$) have a stronger constraint ability on the cosmological parameters than $\Delta\tau$ or $\sigma^{2}$ separately. Here we first propose that this $\Delta\tau/\sigma^{2}$ method can be applied to the strongly lensed systems observed in both GW and EM windows. Combining the redshifts, images, and $\sigma$ observed in the EM domain with the very precise $\Delta\tau$ derived from lensed GW signals, we expect that accurate multi-messenger cosmology can be achieved in the era of third-generation gravitational-wave detectors. Comparing with the constraints from the $\Delta\tau$ method, we prove that using $\Delta\tau/\sigma^{2}$ can improve the discrimination between cosmological models. Furthermore, we demonstrate that with several tens of strongly lensed GW-EM systems, one may reach a constraint on the dark energy equation of state $w$ comparable to the 580 Union2.1 Type Ia supernovae data. Much more stringent constraints on $w$ may be obtained when combining the $\Delta\tau$ and $\Delta\tau/\sigma^{2}$ methods.
J. Wei and X. Wu
Fri, 14 Jul 17
8/55
Comments: 7 pages, 4 figures, resubmitted version