Recently it was shown that the inclusion of higher signal harmonics in the
inspiral signals of binary supermassive black holes (SMBH) leads to dramatic
improvements in parameter estimation with the Laser Interferometer Space
Antenna (LISA). In particular, the angular resolution becomes good enough to
identify the host galaxy or galaxy cluster, in which case the redshift can be
determined by electromagnetic means. The gravitational wave signal also
provides the luminosity distance with high accuracy, and the relationship
between this and the redshift depends sensitively on the cosmological
parameters, such as the equation-of-state parameter w=pDE/ρDE of dark energy. With a single binary SMBH event at z<1 having
appropriate masses and orientation, one would be able to constrain w to
within a few percent. We show that, if the measured sky location is folded into
the error analysis, the uncertainty on w goes down by an additional factor of
2-3, leaving weak lensing as the only limiting factor in using LISA as a dark
energy probe.Comment: 11pages, 1 Table, minor changes in text, accepted for publication in
Classical and Quantum Gravity (special issue for proceedings of 7th LISA
symposium