A Hint of a Blue Axion Isocurvature Spectrum?
  It is known that if the Peccei-Quinn symmetry breaking field is displaced
from its minimum during inflation, the axion isocurvature spectrum is
generically strongly blue tilted with a break transition to a flat spectrum. We
fit this spectrum (incorporated into the "vanilla" $\Lambda$-CDM cosmological
model) to the Planck and BOSS DR11 data and find a mild hint for the presence
of axionic blue-tilted isocurvature perturbations. We find the best fit
parameter region is consistent with all of the dark matter being composed of
QCD axions in the context of inflationary cosmology with an expansion rate of
order $10^{8}$ GeV, the axion decay constant of order $10^{13}$ GeV, and the
initial misalignment angle of order unity. Intriguingly, isocurvature with a
spectral break may at least partially explain the low-$\ell$ vs. high-$\ell$
anomalies seen in the CMB data.
