Constraining the dark energy equation of state using LISA observations
  of spinning Massive Black Hole binaries
  Gravitational wave signals from coalescing Massive Black Hole (MBH) binaries
could be used as standard sirens to measure cosmological parameters. The future
space based gravitational wave observatory Laser Interferometer Space Antenna
(LISA) will detect up to a hundred of those events, providing very accurate
measurements of their luminosity distances. To constrain the cosmological
parameters we also need to measure the redshift of the galaxy (or cluster of
galaxies) hosting the merger. This requires the identification of a distinctive
electromagnetic event associated to the binary coalescence. However, putative
electromagnetic signatures may be too weak to be observed. Instead, we study
here the possibility of constraining the cosmological parameters by enforcing
statistical consistency between all the possible hosts detected within the
measurement error box of a few dozen of low redshift (z<3) events. We construct
MBH populations using merger tree realizations of the dark matter hierarchy in
a LambdaCDM Universe, and we use data from the Millennium simulation to model
the galaxy distribution in the LISA error box. We show that, assuming that all
the other cosmological parameters are known, the parameter w describing the
dark energy equation of state can be constrained to a 4-8% level (2sigma
error), competitive with current uncertainties obtained by type Ia supernovae
measurements, providing an independent test of our cosmological model.
