  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.
