Decline of the Space Density of Quasars between z = 2 and z = 4

We define a new complete sample of 13 optically luminous radio quasars [M_AB(1450 Å) < -26.9 mag and log P_{1.4 GHz}(W Hz^-1) > 25.7] with redshift 3.8 < z < 4.5, obtained by cross-correlating the Faint Images of the Radio Sky at Twenty cm (FIRST) radio survey and the Automatic Plate Measuring Facility catalog of POSS I. We measure the space density to be 1.0 ± 0.3 Gpc^-3, a factor of 1.9 ± 0.7 smaller than the space density of similar quasars at z ≈ 2 (FIRST Bright Quasar Survey). Using a new measurement of the radio-loud fraction of quasars, we find that at z = 4 the total space density of quasars with M_AB(1450 Å) < -26.9 mag is 7.4 ± 2.6 Gpc^-3. This is a factor of 1.8 ± 0.8 less than the space density at z ≈ 2, found by the Two-Degree Field quasar survey. This z = 2/z = 4 ratio, consistent with that of the radio-loud quasars, is significantly different from the ratio of ~10 found for samples including lower luminosity quasars. This suggests that the decline of the space density beyond z ≈ 2 is slower for optically luminous quasars than for less luminous ones.