same time, the infalling gas fuelling the starburst is also feeding the central black hole. After some time the quasar becomes optically visible (unobscured), and soon after that the on-going star formation is quenched on a short time-scale, perhaps via radiative or mechanical feedback from the central engine (see Fabian 2012 for a review). The cosmic star-formation history is shown to be similar to the evolving luminosity density of quasars (which is related to the BH accretion history) at most redshifts (e.g., Boyle & Terlevich 1998; Franceschini et al. 1999; Merloni et al. 2004; Shankar et al. 2007; Silverman et al. 2008; Wall, Pope & Scott 2008), which adds further support to this picture of the galaxy - black hole connection.

In this paper, we probe the co-evolution of black hole growth and star-formation activity using a cross-correlation analysis between optically selected Type 1 quasars over the redshift range $0.2<z<3.5$ and the cosmic infrared background (CIB) in the far-infrared (FIR)/sub-millimetre (sub-mm). The former represents some of the most luminous and massive black holes found to date. The latter is dominated by emission from dusty star-forming galaxies (DSFGs) over a similar redshift range to the quasars (Valiante et al. 2009; Bethermin 