We present the largest high-redshift (3<z<6.85) sample of X-ray-selected active galactic nuclei (AGN) on a contiguous field, using sources detected in the Chandra COSMOS Legacy survey. The sample contains 174 sources, 87 with spectroscopic redshift, the other 87 with photometric redshift (z_phot). In this work we treat z_phot as a probability weighted sum of contributions, adding to our sample the contribution of sources with z_phot<3 but z_phot probability distribution >0 at z>3. We compute the number counts in the observed 0.5-2 keV band, finding a decline in the number of sources at z>3 and constraining phenomenological models of X-ray background. We compute the AGN space density at z>3 in two different luminosity bins. At higher luminosities (logL(2-10 keV) > 44.1 erg/s) the space density declines exponentially, dropping by a factor ~20 from z~3 to z~6. The observed decline is ~80% steeper at lower luminosities (43.55 erg/s < logL(2-10 keV) < 44.1 erg/s), from z~3 to z~4.5. We study the space density evolution dividing our sample in optically classified Type 1 and Type 2 AGN. At logL(2-10 keV) > 44.1 erg/s, unobscured and obscured objects may have different evolution with redshift, the obscured component being three times higher at z~5. Finally, we compare our space density with predictions of quasar activation merger models, whose calibration is based on optically luminous AGN. These models significantly overpredict the number of expected AGN at logL(2-10 keV) > 44.1 erg/s with respect to our data.
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