  The two fundamental assumptions of the standard cosmological model - that the
initial fluctuations are statistically isotropic and Gaussian - are rigorously
tested using maps of the cosmic microwave background (CMB) anisotropy from the
Planck satellite. Deviations from isotropy have been found and demonstrated to
be robust against component separation algorithm, mask choice and frequency
dependence. Many of these anomalies were previously observed in the WMAP data,
and are now confirmed at similar levels of significance (about 3 sigma).
However, we find little evidence for non-Gaussianity, with the exception of a
few statistical signatures that seem to be associated with specific anomalies.
In particular, we find that the quadrupole-octopole alignment is also connected
to a low observed variance of the CMB signal. A power asymmetry is now found to
persist to scales corresponding to about l=600, and can be described in the
low-l regime by a phenomenological dipole modulation model. However, any
primordial power asymmetry is strongly scale-dependent and does not extend to
arbitrarily small angular scales. Finally, it is plausible that some of these
features may be reflected in the angular power spectrum of the data, which
shows a deficit of power on similar scales. Indeed, when the power spectra of
two hemispheres defined by a preferred direction are considered separately, one
shows evidence for a deficit in power, while its opposite contains oscillations
between odd and even modes that may be related to the parity violation and
phase correlations also detected in the data. Although these analyses represent
a step forward in building an understanding of the anomalies, a satisfactory
explanation based on physically motivated models is still lacking.
