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Cosmic variance of $z>7$ galaxies: Prediction from BlueTides

In the coming decade, a new generation of telescopes, including JWST and WFIRST, will probe the period of the formation of first galaxies and quasars, and open up the last frontier for structure formation. Recent simulations as well as observations have suggested that these galaxies are strongly clustered (with large scale bias $\gtrsim6$), and therefore have significant cosmic variance. In this work, we use \texttt{BlueTides}, the largest volume cosmological simulation of galaxy formation, to directly estimate the cosmic variance for current and upcoming surveys. Given its resolution and volume, \texttt{BlueTides} can probe the bias and cosmic variance of $z>7$ galaxies between magnitude $M_{UV}\sim-16$ to $M_{UV}\sim-22$ over survey areas $\sim0.1\ \mathrm{arcmin}^2$ to $\sim 10~\mathrm{deg}^2$. Within this regime, the cosmic variance decreases with survey area/ volume as a power law with exponents between $\sim-0.25$ to $\sim-0.45$. For the planned $10~\mathrm{deg}^2$ field of WFIRST, the cosmic variance is between $3\%$ to $10\%$. Upcoming JWST medium/ deep surveys with areas up to $A\sim100\ \mathrm{arcmin}^2$ will have cosmic variance ranging from $\sim 20-50\%$. Lensed surveys have the highest cosmic variance $\gtrsim 40\%$; the cosmic variance of $M_{UV}\lesssim-16$ galaxies is $\lesssim100\%$ up to $z\sim11$. At higher redshifts such as $z\sim12~(14)$, effective volumes of $\gtrsim(8~\mathrm{Mpc}/h)^3$ ($\gtrsim(12\ \mathrm{Mpc}/h)^3$) are required to limit the cosmic variance to within $100\%$. Finally, we find that cosmic variance is larger than Poisson variance and forms the dominant component of the overall uncertainty in all current and upcoming surveys. We present our calculations in the form of simple fitting functions and an online cosmic variance calculator (CV_AT_COSMIC_DAWN) which we publicly release.