Cosmic Microwave Background Acoustic Peak Locations

TL;DR

This paper analyzes the precise locations of acoustic peaks in the cosmic microwave background power spectra measured by Planck, comparing them with theoretical expectations from the ΛCDM model and exploring the physical effects influencing these locations.

Contribution

It provides a detailed quantitative analysis of the factors affecting acoustic peak locations and confirms their consistency with ΛCDM predictions using Planck data.

Findings

Peak locations agree with ΛCDM expectations.

Differences in simple models vs. numerical calculations are explained.

Physical effects like neutrino free-streaming influence peak positions.

Abstract

The Planck collaboration has measured the temperature and polarization of the cosmic microwave background well enough to determine the locations of eight peaks in the temperature (TT) power spectrum, five peaks in the polarization (EE) power spectrum and twelve extrema in the cross (TE) power spectrum. The relative locations of these extrema give a striking, and beautiful, demonstration of what we expect from acoustic oscillations in the plasma; e.g., that EE peaks fall half way between TT peaks. We expect this because the temperature map is predominantly sourced by temperature variations in the last scattering surface, while the polarization map is predominantly sourced by gradients in the velocity field, and the harmonic oscillations have temperature and velocity 90 degrees out of phase. However, there are large differences in expectations for extrema locations from simple analytic models vs. numerical calculations. Here we quantitatively explore the origin of these differences in gravitational potential transients, neutrino free-streaming, the breakdown of tight coupling, the shape of the primordial power spectrum, details of the geometric projection from three to two dimensions, and the thickness of the last scattering surface. We also compare the peak locations determined from Planck measurements to expectations under the $\Lambda$CDM model. Taking into account how the peak locations were determined, we find them to be in agreement.