Test for anisotropy in the mean of the CMB temperature fluctuation in
  spherical harmonic space
  The standard models of inflation predict statistically homogeneous and
isotropic primordial fluc- tuations, which should be tested by observations. In
this paper we test the statistical isotropy of the mean of the CMB temperature
fluctuations measured by the WMAP in the spherical harmonic space. A classical
method to test a mean, like the simple student's-t test, is not appropriate for
this purpose because the WMAP data contain anisotropic instrumental noise and
suffer from the effect of the mask for the foreground emissions which breaks
the statistical independence. Here we perform a band-power analysis with
Monte-Carlo simulations in which we take into account the anisotropic noise and
the mask. We find evidence of a non-zero mean at 99.93 % confidence level in a
particular range of multipoles. The evidence against the zero-mean assumption
as a whole is still significant at the 99 % confidence level even if the fact
is taken into account that we have tested multiple ranges.
