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Based on recent observations of the cosmic microwave background (CMB), claimsof statistical anomalies in the properties of the CMB fluctuations have beenmade. Although the statistical significance of the anomalies remains only atthe $\sim2-3\sigma$ significance level, the fact that there are many differentanomalies, several of which support a possible deviation from statisticalisotropy, has motivated a search for models that provide a common mechanism togenerate them. The goal of this paper is to investigate whether these anomaliescould originate from non-Gaussian cosmological models, and to determine whatproperties these models should have. We present a simple isotropic,non-Gaussian class of toy models that can reproduce six of the most extensivelystudied anomalies. We compare the presence of anomalies found in simulated mapsgenerated from the toy models and from a standard model with Gaussianfluctuations. We show that the following anomalies, as found in the Planckdata, commonly occur in the toy model maps: (1) large-scale hemisphericalasymmetry (large-scale dipolar modulation), (2) small-scale hemisphericalasymmetry (alignment of the spatial distribution of CMB power over all scales$\ell=[2,1500]$) , (3) a strongly non-Gaussian hot or cold spot, (4) a lowpower spectrum amplitude for $\ell<30$, including specifically (5) a lowquadrupole and an unusual alignment between the quadrupole and the octopole,and (6) parity asymmetry of the lowest multipoles. We note that this class oftoy model resembles models of primordial non-Gaussianity characterised bystrongly scale-dependent $g_{NL}$-like trispectra.

Isotropic non-Gaussian $g_\mathrm{NL}$-like toy models that reproduce the cosmic microwave background anomalies