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Observed scatter in the Lyman-alpha opacity of quasar sightlines at $z<6$ hasmotivated measurements of the correlation between Ly$\alpha$ opacity and galaxydensity, as models that predict this scatter make strong and sometimes oppositepredictions for how they should be related. Our previous work associated twohighly opaque Ly$\alpha$ troughs at $z\sim5.7$ with a deficit of Lyman-$\alpha$emitting galaxies (LAEs). In this work, we survey two of the most highlytransmissive lines of sight at this redshift, towards the $z=6.02$ quasar SDSSJ1306+0356 and the $z=6.17$ quasar PSO J359-06. We find that both fields areunderdense in LAEs within 10 $h^{-1}$ Mpc of the quasar sightline, somewhatless extensive than underdensities associated with Ly$\alpha$ troughs. Wecombine our observations with three additional fields from the literature, andfind that while fields with extreme opacities are generally underdense,moderate opacities span a wider density range. The results at high opacitiesare consistent with models that invoke UV background fluctuations and/or latereionization to explain the observed scatter in IGM Ly$\alpha$ opacities. Thereis tension at low opacities, however, as the models tend to associate lower IGMLy$\alpha$ opacities with higher densities. Although the number of fieldssurveyed is still small, the low-opacity results may support a scenario inwhich the ionizing background in low-density regions increases more rapidlythan some models suggest after becoming ionized. Elevated gas temperatures fromrecent reionization may also be making these regions more transparent.

The relationship between IGM Lyman-alpha opacity and galaxy density near the end of reionization