I'm interested in trying to understand the physical mechanisms that drive the rapid change in space density with cosmic epoch that we observe for QSOs (or quasars) and active galaxies, and in linking that to our current ideas about how galaxies formed. This is work that started with Pippa Goldschmidt in Edinburgh, and then carried on at Oxford with Will Percival and Ana Babic.
It does appear that one of the major drivers for the cosmological
evolution of quasars is the rate at which their host galaxies form.
This in turn is dependent on the hierarchical growth of massive objects
under the influence of gravity. A good starting point for understanding
quasar evolution, then, is to be able to calculate the rate at which
dark matter halos associated with galaxies form as a function of cosmic
epoch. We have studied this using a flawed but useful
analytic prescription known as "extended Press-Schechter theory".
The diagram on the left shows how the integrated luminosity emitted per unit volume in the universe (shown logarithmically on the y-axis) has varied with cosmic epoch (as measured by redshift, on the x-axis: at redshift z the Universe was a factor (1+z) smaller and was younger by a comparable factor: this expansion of the volume of the universe has been corrected for in the luminosity density). The lower dashed red curve shows the result of the calculation of the expected luminosity density if supermassive black holes grow at the same rate as the dark-matter 'halos' of their host galaxies. The blue points and curve shows the result of the measurement of the luminosity density from X-ray surveys of quasars and active galaxies. (see reference 2 in the list below for further details). There is excellent agreement until redshifts close to zero, corresponding to the present day, when the observed luminosity density appears to fall below the prediction by a factor two.
Having got part of the way with that work, we now need to understand the relationship between those dark matter halos, their galaxies of stars, and the black holes that form within them. Oh, plus of course how the accretion of matter onto the black hole, which controls the luminous output, is affected by environment and by cosmic epoch. Hence as well as studying formation rate, we also need to study quasar host galaxies, make estimates of black hole mass in those galaxies, and try to understand the detailed distribution of quasar luminosities in the universe.