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The QSO luminosity function at z>5 provides strong constraints on models ofjoint evolution of QSO and their hosts. However, these observations arechallenging because the low space densities of these objects necessitatesurveying of large areas, in order to obtain statistically meaningful samples,while at the same time cosmological redshifting and dimming means that ratherdeep Near Infrared (NIR) imaging must be carried out. Several upcoming andproposed facilities with wide-field NIR imaging capabilities will open up thisnew region of parameter space. In this paper we present predictions for theexpected number counts of z>5 QSOs, based on simple empirical andsemi-empirical models of QSO evolution, as a function of redshift, depth andsurveyed area. We compute the evolution of observed-frame QSO magnitudes andcolors in a representative photometric system covering the wavelength range550nm<lambda<1800nm, and combine this information with different estimates forthe evolution of the QSO luminosity function. We conclude that plannedground-based surveys such as Pan-STARRS and VISTA should be able to detect alarge number of luminous QSOs up to z<7.5, but that space-based missions suchas EUCLID (formerly SPACE/DUNE) or SNAP are probably required in order toobtain substantial samples at higher redshift. We also use our models topredict the expected number counts for future X-ray space missions (such asXEUS and Constellation-X), and show that because of their small field-of-view,these telescopes are unlikely to discover significant numbers of AGN at veryhigh redshift. However, X-ray follow-up of objects detected at longerwavelength will be an important means of confirming their identity as AGN andconstraining obscuration.

Expected z>5 QSO number counts in large area deep near-infrared surveys