Testable polarization predictions for models of CMB isotropy anomalies

Anomalies in the large-scale cosmic microwave background (CMB) temperature sky measured by the Wilkinson Microwave Anisotropy Probe have been suggested as possible evidence for a violation of statistical isotropy on large scales. In any physical model for broken isotropy, there are testable consequences for the CMB polarization field. We develop simulation tools for predicting the polarization field in models that break statistical isotropy locally through a modulation field. We study two different models: dipolar modulation, invoked to explain the asymmetry in power between northern and southern ecliptic hemispheres, and quadrupolar modulation, posited to explain the alignments between the quadrupole and octopole. For the dipolar case, we show that predictions for the correlation between the first 10 multipoles of the temperature and polarization fields can typically be tested at better than the 98% CL. For the quadrupolar case, we show that the polarization quadrupole and octopole should be moderately aligned. Such an alignment is a generic prediction of explanations which involve the temperature field at recombination and thus discriminate against explanations involving foregrounds or local secondary anisotropy. Predicted correlations between temperature and polarization multipoles out to $\ell =5$ provide tests at the $\sim 99\%$ CL or stronger for quadrupolar models that make the temperature alignment more than a few percent likely. As predictions of anomaly models, polarization statistics move beyond the a posteriori inferences that currently dominate the field.