Bias in low-multipole CMB reconstructions
  The large-angle, low multipole cosmic microwave background (CMB) provides a
unique view of the largest angular scales in the Universe. Study of these
scales is hampered by the facts that we have only one Universe to observe, only
a few independent samples of the underlying statistical distribution of these
modes, and an incomplete sky to observe due to the interposing Galaxy.
Techniques for reconstructing a full sky from partial sky data are well known
and have been applied to the large angular scales. In this work we critically
study the reconstruction process and show that, in practise, the reconstruction
is biased due to leakage of information from the region obscured by foregrounds
to the region used for the reconstruction. We conclude that, despite being
suboptimal in a technical sense, using the unobscured region without
reconstructing is the most robust measure of the true CMB sky. We also show
that for noise free data reconstructing using the usual optimal, unbiased
estimator may be employed without smoothing thus avoiding the leakage problem.
Unfortunately, directly applying this to real data with noise and residual,
unmasked foregrounds yields highly biased reconstructions requiring further
care to apply this method successfully to real-world CMB.
