Variograms of the Cosmic Microwave Background Temperature Fluctuations:
  Confirmation of Deviations from Statistical Isotropy
  The Standard Inflationary model predicts an isotropic distribution of the
Cosmic Microwave Background temperature fluctuations. Detection of deviations
from statistical isotropy would call for a revision of the physics of the early
universe. This paper introduces the variogram as a powerful tool to detect and
characterize deviations from statistical isotropy in Cosmic Microwave
Background maps. Application to the Wilkinson Microwave Anisotropy Probe data
clearly shows differences between the northern and the southern hemispheres.
The sill and range of the northern hemisphere's variogram are lower than those
of the southern hemisphere. Moreover the variogram for the northern hemisphere
lies outside the 99% c.l. for scales above ten degrees. Differences between the
northern and southern hemispheres in the functional dependence of the variogram
with the scale can be used as a validation bench mark for proposed anisotropic
cosmological models.
