The large-scale modulation of the density distribution in standard   axionic CDM and its cosmological and physical impact
  It is shown, that the energy density of coherent axion field oscillations in the cosmology of standard invisible axion should be distributed in the Universe in the form of archioles, being nonlinear inhomogeneous structure, reflecting the large scale distribution of Brownian structure of axion strings in the very early Universe. Spectrum of inhomogeneities, generated by archioles, is obtained and their effects in the spectrum and quadrupole anisotropy of relic radiation are considered. The axionic-string-decay-model-independent restriction on the scale of axion interaction is obtained. 
M.Yu.Khlopov, A.S.Sakharov, D.D.Sokoloff