Exploring the distance-redshift relation with gravitational wave
  standard sirens and tomographic weak lensing
  Gravitational waves from inspiraling compact objects provide us with
information of the distance scale since we can infer the absolute luminosity of
the source from analysis of the wave form, which is known as standard sirens.
The first detection of the gravitational wave signal of the binary black hole
merger event by Advanced LIGO has opened up the possibility of utilizing
standard sirens as cosmological probe. In order to extract information of the
distance-redshift relation, we cross-correlate weak lensing, which is an
unbiased tracer of matter distribution in the Universe, with the projected
number density of gravitational wave sources. For weak lensing, we employ
tomography technique to efficiently obtain information of large-scale
structures at wide ranges of redshifts. Making use of the cross-correlations
along with the auto-correlations, we present forecast of constraints on four
cosmological parameters, i.e., Hubble parameter, matter density, the equation
of state parameter of dark energy, and the amplitude of matter fluctuation. To
fully explore the ability of cross-correlations, which require large
overlapping sky coverage, we consider the specific case with the upcoming
surveys by \textit{Euclid} for weak lensing and Einstein Telescope for standard
sirens. We show that cosmological parameters can be tightly constrained solely
by these auto- and cross-correlations of standard sirens and weak lensing. For
example, the $1\text{-}\sigma$ error of Hubble parameter is expected to be
$\sigma (H_0) = 0.33 \, \mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$.
Thus, the proposed statistics will be a promising probe into the distance
scale.
