  We present local extrema studies of two models that introduce a preferred
direction into the observed cosmic microwave background (CMB) temperature
field. In particular, we make a frequentist comparison of the one- and
two-point statistics for the dipole modulation and ACW models with data from
the five-year Wilkinson Microwave Anisotropy Probe (WMAP). This analysis is
motivated by previously revealed anomalies in the WMAP data, and particularly
the difference in the statistical nature of the temperature anisotropies when
analysed in hemispherical partitions.
  The analysis of the one-point statistics indicates that the previously
determined hemispherical variance difficulties can be apparently overcome by a
dipole modulation field, but new inconsistencies arise if the mean and the
l-dependence of the statistics are considered. The two-point correlation
functions of the local extrema, the temperature pair product and the
point-point spatial pair-count, demonstrate that the impact of such a
modulation is to over-`asymmetrise' the temperature field on smaller scales
than the wave-length of the dipole or quadrupole, and this is disfavored by the
observed data.The results from the ACW model predictions, however, are
consistent with the standard isotropic hypothesis. The two-point analysis
confirms that the impact of this type of violation of isotropy on the
temperature extrema statistics is relatively weak.
  From this work, we conclude that a model with more spatial structure than the
dipole modulated or rotational-invariance breaking models are required to fully
explain the observed large-scale anomalies in the WMAP data.

Cosmology and Nongalactic Astrophysics