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The most distinctive feature of the primordial density inhomogeneities thatexisted in the cosmic plasma at the instant of decoupling is their scaleinvariant power spectrum ${\cal P}(k) \sim k$ over the range $k \ll H_{eq}$ ofmodes with cosmologically large comoving wavelength. We characterize thisfeature in real space, in terms of their correlation function at two points. Weshow that over cosmologically large comoving distances $r \gg H^{-1}_{eq}$ theprimordial inhomogeneities were (anti)correlated as $f(r) \sim - r^{-4}$. Werevisit the so-called {\it origin of structures problem} of the standardcosmology at the light of this observation. Our conclusions contradict thecurrent wisdom on this issue.

Generation of primordial cosmological density inhomogeneities with scale  invariant power spectrum during the standard radiation dominated expansion of  the universe