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

TL;DR

This paper demonstrates that the acoustic peaks in the CMB can be explained by standard causal boundary conditions within Friedmann-Robertson-Walker cosmology, offering an alternative to inflationary models for structure formation.

Contribution

It shows that the acoustic peaks and scale invariance of primordial density anisotropies can be derived from causality and boundary conditions without invoking inflation.

Findings

Acoustic peaks arise from causal horizon boundary conditions.

Primordial density anisotropies are discrete harmonic modes.

Provides an alternative explanation to inflation for structure origin.

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.