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 (MAB(1450Å)< −26. 9 and log P1.4GHz(WHz−1) > 25.7) with redshift 3.8 < z < 4.5, obtained by crosscorrelating 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 (FBQS). Using a new measurement of the radio-loud fraction of quasars we find that at z = 4 the total space density of quasars with MAB(1450Å)< −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 ∼ 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. Subject headings: cosmology: observations, early-universe, galaxies: evolution, galaxies: formation, quasars: general, surveys