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 Angstrom) < -26.9 mag and log P_1.4 GHz(W/Hz) > 25.7 with redshift 3.8 < z < 4.5, obtained by cross-correlating the FIRST radio survey and the APM catalogue of POSS-I. We measure the space density to be 1.0 +/- 0.3 /Gpc^3, a factor 1.9 +/- 0.7 smaller than the space density of similar quasars at z=2. 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 Angstrom) < -26.9 is 7.4 +/- 2.6/Gpc^3. This is a factor 1.8 +/- 0.8 less than the space density at z=2, found by the 2dF quasar survey. This (z=2)/(z=4) ratio, consistent with that of the radio-loud quasars, is significantly different from the ratio of about 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.