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Cosmic Microwave Background (CMB) full-sky temperature data show ahemispherical asymmetry in power nearly aligned with the Ecliptic. In realspace, this anomaly can be quantified by the temperature variance in thenorthern and southern Ecliptic hemispheres. In this context, the northernhemisphere displays an anomalously low variance while the southern hemisphereappears unremarkable (consistent with expectations from the best-fittingtheory, $\Lambda$CDM). While this is a well established result in temperature,the low signal-to-noise ratio in current polarization data prevents a similarcomparison. This will change with a proposed ground-based CMB experiment,CMB-S4. With that in mind, we generate realizations of polarization mapsconstrained by the temperature data and predict the distribution of thehemispherical variance in polarization considering two different sky coveragescenarios possible in CMB-S4: full Ecliptic north coverage and just the portionof the North that can be observed from a ground based telescope at the highChilean Atacama plateau. We find that even in the set of realizationsconstrained by the temperature data, the low northern hemisphere varianceobserved in temperature is not expected in polarization. Therefore, ananomalously low variance detection in polarization would provide strongevidence against the hypothesis that the temperature anomaly is simply astatistical fluke. We show, within $\Lambda$CDM, how variance measurements inboth sky coverage scenarios are related. We find that the variance makes for agood statistic in cases where the sky coverage is limited, however a fullnorthern coverage is still preferable.

CMB-S4 and the Hemispherical Variance Anomaly