Determination of Dark Energy by the Einstein Telescope: Comparing with
  CMB, BAO and SNIa Observations
  A design study is currently in progress for a third generation
gravitational-wave (GW) detector called Einstein Telescope (ET). An important
kind of source for ET will be the inspiral and merger of binary neutron stars
(BNS) up to $z \sim 2$. If BNS mergers are the progenitors of short-hard
$\gamma$-ray bursts, then some fraction of them will be seen both
electromagnetically and through GW, so that the luminosity distance and the
redshift of the source can be determined separately. An important property of
these `standard sirens' is that they are \emph{self-calibrating}: the
luminosity distance can be inferred directly from the GW signal, with no need
for a cosmic distance ladder. Thus, standard sirens will provide a powerful
independent check of the $\Lambda$CDM model. In previous work, estimates were
made of how well ET would be able to measure a subset of the cosmological
parameters (such as the dark energy parameter $w_0$) it will have access to,
assuming that the others had been determined to great accuracy by alternative
means. Here we perform a more careful analysis by explicitly using the
potential Planck CMB data as prior information for these other parameters. We
find that ET will be able to constrain $w_0$ and $w_a$ with accuracies $\Delta
w_0 = 0.099$ and $\Delta w_a = 0.302$, respectively. These results are compared
with projected accuracies for the JDEM Baryon Acoustic Oscillations project and
the SNAP Type Ia supernovae observations.
