High-redshift quasars in the Cold Dark Matter cosmogony

We argue that the observed space density of luminous quasars between z = 2 and z = 4 is compatible with the cold dark matter (CDM) model if quasars are short lived and radiate at about the Eddington limit. However, according to the CDM model the abundance of high luminosity quasars must decline exponentially at higher redshifts. Even if all proto-galaxies form quasars, and about 1% of the baryons within a protogalaxy collapse into a compact object, we would expect a steep fall in the density of quasars with L > 1047ergs−1 at redshifts z ≳ 5. The existence of a cut-off in the quasar numbers at high redshift could therefore supply an important test of the CDM theory.