Statistical Characterization of Temperature Patterns in Anisotropic
  Cosmologies
  We consider the issue of characterizing the coherent large-scale patterns
from CMB temperature maps in globally anisotropic cosmologies. The methods we
investigate are reasonably general; the particular models we test them on are
the homogeneous but anisotropic relativistic cosmologies described by the
Bianchi classification. Although the temperature variations produced in these
models are not stochastic, they give rise to a "non-Gaussian" distribution of
temperature fluctuations over the sky that is a partial diagnostic of the
model. We explore two methods for quantifying non-Gaussian and/or
non-stationary fluctuation fields in order to see how they respond to the
Bianchi models.We first investigate the behavior of phase correlations between
the spherical harmonic modes of the maps. Then we examine the behavior of the
multipole vectors of the temperature distribution which, though defined in
harmonic space, can indicate the presence of a preferred direction in real
space, i.e. on the 2-sphere. These methods give extremely clear signals of the
presence of anisotropy when applied to the models we discuss, suggesting that
they have some promise as diagnostics of the presence of global asymmetry in
the Universe.
