Missing large-angle correlations versus even-odd point-parity imbalance
  in the cosmic microwave background
  Context. The existence of a maximum correlation angle ($\theta_{max} \gtrsim
60^{\circ}$) in the two-point angular temperature correlations of cosmic
microwave background (CMB) radiation, measured by WMAP and Planck, stands in
sharp contrast to the prediction of standard inflationary cosmology, in which
the correlations should extend across the full sky (i.e., $180^{\circ}$). The
introduction of a hard lower cutoff ($k_{min}$) in the primordial power
spectrum, however, leads naturally to the existence of $\theta_{max}$. Among
other cosmological anomalies detected in these data, an apparent dominance of
odd-over-even parity multipoles has been seen in the angular power spectrum of
the CMB. This feature, however, may simply be due to observational
contamination in certain regions of the sky.
  Aims. In attempting to provide a more detailed assessment of whether this
odd-over-even asymmetry is intrinsic to the CMB, we therefore proceed in this
paper, first, to examine whether this odd-even parity imbalance also manifests
itself in the angular correlation function and, second, to examine in detail
the interplay between the presence of $\theta_{max}$ and this observed anomaly.
  Methods. We employed several parity statistics and recalculated the angular
correlation function for different values of the cutoff $k_{min}$ in order to
optimize the fit to the different Planck 2018 data.
  Results. We find a phenomenological connection between these features in the
data, concluding that both must be considered together in order to optimize the
theoretical fit to the Planck 2018 data.
  Conclusions. This outcome is independent of whether the parity imbalance is
intrinsic to the CMB, but if it is, the odd-over-even asymmetry would clearly
point to the emergence of new physics.
