A snapshot survey for gravitational lenses among z ≥ 4.0 quasars. II. Constraints on the 4.0 < z < 5.4 quasar population

We report on i-band snapshot observations of 157 Sloan Digital Sky Survey quasars at 4.0 < z < 5.4 using the Advanced Camera for Surveys on the Hubble Space Telescope (HST) to search for evidence of gravitational lensing of these sources. None of the quasars appear to be strongly lensed and multiply imaged at the angular resolution (∼0″1) and sensitivity of HST. The nondetection of strong lensing in these systems constrains the z = 4-5 luminosity function to an intrinsic slope of β > -3.8(3 σ), assuming a break in the quasar luminosity function at M* ₁₄₅₀ ∼ -24.5. This constraint is considerably stronger than the limit of β > -4.63 obtained from the absence of lensing in four z > 5.7 quasars. Such constraints are important to our understanding of the true space density of high-redshift quasars and the ionization state of the early universe.