Constraints on the cosmic distance duality relation with simulated data
  of gravitational waves from the Einstein Telescope
  The cosmic distance duality relation (CDDR) has been test through several
astronomical observations in the last years. This relation establishes a simple
equation relating the angular diameter ($D_A$) and luminosity ($D_L$) distances
at a redshift $z$, $D_LD_A^{-1}(1+z)^{-2}=\eta=1$. However, only very recently
this relation has been observationally tested at high redshifts ($z \approx
3.6$) by using luminosity distances from type Ia supernovae (SNe Ia) and gamma
ray bursts (GRBs) plus angular diameter distances from strong gravitational
lensing (SGL) observations. The results show that no significant deviation from
the CDDR validity has been verified. In this work, we test the potentialities
of future luminosity distances from gravitational waves (GWs) sources to impose
limit on possible departures of CDDR jointly with current SGL observations. The
basic advantage of $D_L$ from GWs is being insensitive to non-conservation of
the number of photons. By simulating 600, 900 and 1200 data of GWs using the
Einstein Telescope (ET) as reference, we derive limits on $\eta(z)$ function
and obtain that the results will be at least competitive with current limits
from the SNe Ia $+$ GRBs $+$ SGLs analyses.
