Constraining the AGN Luminosity Function from JWST with the X-Ray Background

We predict the X-ray background (XRB) expected from the population of quasars detected by the James Webb Space Telescope spectroscopic surveys over the redshift range z similar to 4-7. We find that the measured UV emissivities imply a similar to 10 times higher unresolved XRB than constrained by current experiments. We illustrate the difficulty of simultaneously matching the faint end of the quasar luminosity function and the XRB constraints. We discuss possible origins and consequences of this discrepancy.