  The tight correlation between the masses of central black holes and their
host spheroids in nearby galaxies and active galactic nuclei suggests that
black hole growth is closely related to their spheroid formation. Based on our
previous work regarding such a joint evolutionary scheme and the consequential
black hole to bulge mass correlation, we use the X-ray luminosity function of
AGN and the cosmological evolution rate which are from ROSAT X-ray surveys to
estimate the cosmic star formation history associated with the black hole
growth. By the Basic assumption that the major black hole growth occurs during
the luminous AGN phase, the luminosity function of AGNs as a function of
redshift traces not only the accretion history of the black holes but also the
cosmic star formation history of the spheroids.
  Although the space density of the especially luminous QSOs is very low, we
show that the total amount of star formation associated with the massive black
hole growth is almost the same as that of Lyman Break Galaxies detected by the
current optical deep surveys. We thus argue that the optical deep surveys may
miss about half of the net star formation in our Universe, This is probably due
to in part significant dust extinction as well as the small field of view of
previous optical surveys which cannot sample such rare events with relatively
short time scale. However, the far infrared emission from the dust heated by
star fomation on-going during the black hole growth could sufficiently account
for the observed SCUBA number counts, and would be the probable dominating
energy source of the SUBA population.
