Contamination cannot explain the lack of large-scale power in the cosmic microwave background radiation

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP. One of these is a lack of large-scale power. Because the data otherwise match standard models extremely well, it is natural to consider perturbations of the standard model as possible explanations. We show that, as long as the source of the perturbation is statistically independent of the source of the primary CMB anisotropy, no such model can explain this large-scale power deficit. On the contrary, any such perturbation always reduces the probability of obtaining any given low value of large-scale power. We rigorously prove this result when the lack of large-scale power is quantified with a quadratic statistic, such as the quadrupole moment. When a statistic based on the integrated square of the correlation function is used instead, we present strong numerical evidence in support of the result. The result applies to models in which the geometry of spacetime is perturbed (e.g., an ellipsoidal Universe) as well as explanations involving local contaminants, undiagnosed foregrounds, or systematic errors. Because the large-scale power deficit is arguably the most significant of the observed anomalies, explanations that worsen this discrepancy should be regarded with great skepticism, even if they help in explaining other anomalies such as multipole alignments.