  CMB full-sky temperature data show a hemispherical asymmetry in power nearly
aligned with the Ecliptic. In real space, this anomaly can be quantified by the
temperature variance in the northern and southern Ecliptic hemispheres, with
the north displaying an anomalously low variance while the south appears
consistent with expectations from the best-fitting theory, LCDM. While this is
a well-established result in temperature, the low signal-to-noise ratio in
current polarization data prevents a similar comparison. Even though
temperature and polarization are correlated, polarization realizations
constrained by temperature data show that the lack of variance is not expected
to be present in polarization data. Therefore, a natural way of testing whether
the temperature result is a fluke is to measure the variance of CMB
polarization components. In anticipation of future CMB experiments that will
allow for high-precision large-scale polarization measurements, we study how
variance of polarization depends on LCDM parameters' uncertainties by
forecasting polarization maps with Planck's MCMC chains. We find that, unlike
temperature variance, polarization variance is noticeably sensitive to present
uncertainties in cosmological parameters. This comes mainly from the current
poor constraints on the reionization optical depth, tau, and the fact that tau
drives variance at low multipoles. In this work we show how the variance of
polarization maps generically depends on the cosmological parameters. We
demonstrate how the improvement in the tau measurement seen between Planck's
two latest data releases results in a tighter constraint on polarization
variance expectations. Finally, we consider even smaller uncertainties on tau
and how more precise measurements of tau can drive the expectation for
polarization variance in a hemisphere close to that of the
cosmic-variance-limited distribution.
