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

The most distinctive feature of the primordial density inhomogeneities that existed in the cosmic plasma at the instant of decoupling is their scale invariant power spectrum $\mathcal{P}(k)\sim k$ over the range $k\ll H_{eq}$ of modes with cosmologically large comoving wavelength. We characterize this feature in real space, in terms of their correlation function at two points. We show that over cosmologically large comoving distances $r\gg H_{eq}^{-1}$ the primordial inhomogeneities were (anti)correlated as $f(r)\sim -r^{-4}$. We revisit the so-called {\it origin of structures problem} of the standard cosmology at the light of this observation. Our conclusions contradict the current wisdom on this issue.