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Cosmic variance introduces significant uncertainties into galaxy numberdensity properties when surveying the high-z Universe with a small volume, suchuncertainties produce the field-to-field variance of galaxy number $\sigma_{g}$in observational astronomy. This uncertainty significantly affects theLuminosity Functions (LF) measurement of Lya Emitters (LAEs). For most previousLya LF studies, $\sigma_{g}$ is often adopted from predictions by cosmologicalsimulations, but barely confirmed by observations. Measuring cosmic variancerequires a huge sample over a large volume, exceeding the capabilities of mostastronomical instruments. In this study, we demonstrate an observationalapproach for measuring the cosmic variance contribution for $z\approx2.2$ LyaLFs. The LAE candidates are observed using narrowband and broadband of theSubaru/Hyper Suprime-Cam (HSC), with 8 independent fields, making the totalsurvey area $\simeq11.62$deg$^2$ and a comoving volume of$\simeq8.71\times10^6$Mpc$^3$. These eight fields are selected using theproject of MAMMOTH. We report a best-fit Schechter function with parameters$\alpha=-1.75$ (fixed), $L_{Ly\alpha}^{*}=5.18_{-0.40}^{+0.43} \times10^{42}$erg s$^{-1}$ and$\phi_{Lya}^{*}=4.87_{-0.55}^{+0.54}\times10^{-4}$Mpc$^{-3}$ for the overallLya LFs. After clipping out the regions that can bias the cosmic variancemeasurements, we calculate $\sigma_{g}$, by sampling LAEs within multiplepointings assigned on the field image. We investigate the relation between$\sigma_{g}$ and survey volume $V$, and fit a simple power law:$\sigma_g=k\times(\frac{V_{\rm eff}}{10^5 {\rm Mpc}^3})^{\beta}$. We findbest-fit values of $-1.209_{-0.106}^{+0.106}$ for $\beta$ and$0.986_{-0.100}^{+0.108}$ for k. We compare our measurements with predictionsfrom simulations and find that the cosmic variance of LAEs might be larger thanthat of general star-forming galaxies.

MAMMOTH-Subaru V. Effects of Cosmic Variance on Ly$\alpha$ Luminosity Functions at $z=2.2-2.3$