Acoustic peaks in the CMB: a matter of standard causal boundary conditions on primordial density anisotropies

Abstract

The pattern of acoustic peaks in the sub-horizon power spectrum of primordial density anisotropies at recombination can be naturally understood in the framework of standard Friedmann-Robertson-Walker cosmology (without inflation) as a consequence of the boundary conditions imposed by the causal horizon on the statistical two-points correlation functions: the sub-horizon spectrum is discrete (harmonic), with comoving modes located at $k_n = n \frac{\pi}{H^{-1}_{eq}}$, $n = 1,2,...$, because the causally connected patch of the universe at recombination is compact, with comoving radius $H^{-1}_{eq}$. The results presented in this paper complement those presented in [1], where it was shown that the scale invariance of the primordial density anisotropies over comoving scales of cosmological size is also a consequence of the boundary conditions imposed by causality. Together these results lay an appealing theoretical alternative to the inflationary paradigm as the ultimate answer for the origin of cosmological structures in standard cosmology.