Test for anisotropy in the mean of the CMB temperature fluctuation in spherical harmonic space

Abstract

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.