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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 $2.5 σ$ and $3.1 σ$ 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.