A Test for the Zero Mean Hypothesis in Cosmology
  One working hypothesis on which analyses of cosmological data are based is
the zero ensemble mean hypothesis, which is related to the statistical
homogeneity of cosmological perturbations. This hypothesis, however, should be
tested by observational data in the current era of precision cosmology. Herein,
we test the hypothesis by analyzing recent, foreground-reduced cosmic microwave
background (CMB) maps, combining the spherical harmonic coefficients of the
masked CMB temperature anisotropies in such a way that the combined variables
can be treated as statistically independent samples. We find evidence against
the zero mean hypothesis in two particular ranges of multipoles, with
significance levels of $2.5 \sigma$ and $3.1 \sigma$ in the multipole ranges of
$\ell \approx 61$-$86$ and $213$-$256$, respectively, for both the Planck and
Wilkinson Microwave Anisotropy Probe maps. The latter signal is consistent with
our previous result found by using brute-force Monte-Carlo simulations.
However, within the method employed in this paper we conclude that the zero
mean hypothesis is consistent with the current CMB data on the basis of
Stouffer's weighted Z statistics, which takes multiple testing into account.
