Cosmography with strong lensing of LISA gravitational wave sources
  LISA might detect gravitational waves from mergers of massive black hole
binaries strongly lensed by intervening galaxies (Sereno et al. 2010). The
detection of multiple gravitational lensing events would provide a new tool for
cosmography. Constraints on cosmological parameters could be placed by
exploiting either lensing statistics of strongly lensed sources or time delay
measurements of lensed gravitational wave signals. These lensing methods do not
need the measurement of the redshifts of the sources and the identification of
their electromagnetic counterparts. They would extend cosmological probes to
redshift z <= 10 and are then complementary to other lower or higher redshift
tests, such as type Ia supernovae or cosmic microwave background. The accuracy
of lensing tests strongly depends on the formation history of the merging
binaries, and the related number of total detectable multiple images. Lensing
amplification might also help to find the host galaxies. Any measurement of the
source redshifts would allow to exploit the distance-redshift test in
combination with lensing methods. Time-delay analyses might measure the Hubble
parameter H_0 with accuracy of >= 10 km s^{-1}Mpc^{-1}. With prior knowledge of
H_0, lensing statistics and time delays might constrain the dark matter density
(delta Omega_M >= 0.08, due to parameter degeneracy). Inclusion of our methods
with other available orthogonal techniques might significantly reduce the
uncertainty contours for Omega_M and the dark energy equation of state.
