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Measurements of the luminosity function of active galactic nuclei (AGN) athigh redshift ($z\gtrsim 6$) are expected to suffer from field-to-fieldvariance, including cosmic and Poisson variances. Future surveys, such as thosefrom the Euclid telescope and James Webb Space Telescope (JWST), will also beaffected by field variance. We use the Uchuu simulation, a state-of-the-artcosmological $N$-body simulation with 2.1 trillion particles in a volume of$25.7~\mathrm{Gpc}^3$, combined with a semi-analytic galaxy and AGN formationmodel, to generate the Uchuu-$\nu^2$GC catalog, publicly available, that allowsus to investigate the field-to-field variance of the luminosity function ofAGN. With this Uchuu-$\nu^2$GC model, we quantify the cosmic variance as afunction of survey area, AGN luminosity, and redshift. In general, cosmicvariance decreases with increasing survey area and decreasing redshift. We findthat at $z\sim6-7$, the cosmic variance depends weakly on AGN luminosity. Thisis because the typical mass of dark matter haloes in which AGN reside does notsignificantly depend on luminosity. Due to the rarity of AGN, Poisson variancedominates the total field-to-field variance, especially for bright AGN. We alsoexamine the effect of parameters related to galaxy formation physics on thefield variance. We discuss uncertainties present in the estimation of thefaint-end of the AGN luminosity function from recent observations, and extendthis to make predictions for the expected number of AGN and their variance forupcoming observations with Euclid, JWST, and the Legacy Survey of Space andTime (LSST).

Uchuu-$\nu^2$GC galaxies and AGN: Cosmic variance forecasts of high-redshift AGN for JWST, Euclid, and LSST