Isotropic non-Gaussian gNL-like toy models that reproduce cosmic microwave background anomalies

Context. Based on recent observations of the cosmic microwave background (CMB), claims of statistical anomalies in the properties
of the CMB fluctuations have been made. Although the statistical significance of the anomalies remains only at the ∼2−3σ significance level, the fact that there are many different anomalies, several of which support a possible deviation from statistical isotropy,
has motivated a search for models that provide a common mechanism to generate them.
Aims. The goal of this paper is to investigate whether these anomalies could originate from non-Gaussian cosmological models, and
to determine what properties these models should have.
Methods. We present a simple isotropic, non-Gaussian class of toy models that can reproduce six of the most extensively studied
anomalies. We compare the presence of anomalies found in simulated maps generated from the toy models and from a standard model
with Gaussian fluctuations.
Results. We show that the following anomalies, as found in the Planck data, commonly occur in the toy model maps: (1) large-scale
hemispherical asymmetry (large-scale dipolar modulation), (2) small-scale hemispherical asymmetry (alignment of the spatial distribution of CMB power over all scales l = [2, 1500]), (3) a strongly non-Gaussian hot or cold spot, (4) a low power spectrum amplitude
for l < 30, including specifically (5) a low quadrupole and an unusual alignment between the quadrupole and the octopole, and (6)
parity asymmetry of the lowest multipoles. We note that this class of toy model resembles models of primordial non-Gaussianity
characterised by strongly scale-dependent gNL-like trispectra