  Binary black hole coalescences emit gravitational waves that will be
measurable by the space-based detector it LISA to large redshifts. This
suggests that LISA may be able to observe black holes grow and evolve as the
universe evolves, mapping the distribution of black hole masses as a function
of redshift. An immediate difficulty with this idea is that LISA measures
certain redshifted combinations of masses with good accuracy: if a system has
some mass parameter m, then LISA measures (1+z)m. This mass-redshift degeneracy
makes it difficult to follow the mass evolution. In many cases, LISA will also
measure the luminosity distance D of a coalescence accurately. Since
cosmological parameters (particularly the mean density, the cosmological
constant, and the Hubble constant) are now known with moderate precision, we
can obtain z from D and break the degeneracy. This makes it possible to
untangle the mass and redshift and to study the mass and merger history of
black holes. Mapping the black hole mass distribution could open a window onto
an early epoch of structure formation.
