What the small angle CMB really tells us about the curvature of the
  Universe
  It is well known that observations of the cosmic microwave background (CMB)
are highly sensitive to the spatial curvature of the Universe, k. Here we find
that what is in fact being tightly constrained by small angle fluctuations is
spatial curvature near the surface of last scattering, and that if we allow k
to be a function of position, rather than taking a constant value everywhere,
then considerable spatial curvature is permissible within our own locale. This
result is of interest for the giant void models that attempt to explain the
supernovae observations without Dark Energy. We find voids models with a
homogeneous big bang can be compatible with the observed small angle CMB, but
only if they exist in a positively curved universe. To be compatible with local
measurements of H_0, however, we find that a radially varying bang time is
required.
