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

TL;DR

This paper analyzes the scale-invariant primordial density fluctuations in the early universe, revealing their correlation properties and challenging existing views on structure formation.

Contribution

It characterizes the real-space correlation function of primordial inhomogeneities with a scale-invariant spectrum, providing new insights into their large-scale correlations and implications for structure origin.

Findings

Primordial inhomogeneities exhibit a correlation function decaying as -r^{-4} at large scales.

The results challenge current understanding of the origin of cosmic structures.

The scale-invariant spectrum implies specific correlation properties over large distances.

Abstract

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 ${\cal P}(k) \sim k$ 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 $r \gg H^{-1}_{eq}$ 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.