Strong Evidence Against a Statistically Isotropic Universe

The standard cosmological model predicts statistically isotropic cosmic microwave background (CMB) fluctuations characterized by the CMB temperature coefficients $a_{\ell m}$ being independent Gaussian random variables with zero mean and with variance that depends only on $\ell$. However, several summary statistics of CMB isotropy have anomalous values, including: the low level of large-angle temperature correlations, $S_{1/2}$; the excess power in odd versus even low-$\ell$ multipoles, $R^{TT}$; the (low) variance of large-scale temperature anisotropies in the ecliptic north, but not the south, $\sigma^2_{16}$; and the alignment and planarity of the quadrupole and octopole of temperature, $S_{QO}$. Individually, their low $p$-values are weak evidence for violation of statistical isotropy. We study the tail values of these statistics and find very little correlation among them. We show that the joint probability of all four anomalies occurring by chance in $\Lambda$CDM is likely $\leq3\times10^{-8}$. We examine the balance in the impact of look-elsewhere effects and the existence of other anomalies on the significance of this result. We argue that non-Gaussianity alone is unlikely to account for the anomalies seen at the level of the angular power spectrum, $C_\ell$, and that they instead appear to require correlations between $a_{\ell m}$. Our results provide strong evidence for a violation of statistical isotropy, and we conclude that the anomalies should not be dismissed as flukes within $\Lambda$CDM.