The spectrum of axions in a scaling string network

TL;DR

This paper investigates the axion spectrum emitted by cosmic string networks, demonstrating near scale-invariance and providing detailed results on the energy spectrum and axion number density relevant for axion dark matter searches.

Contribution

It introduces a comprehensive analysis of axion spectra from scaling string networks, including a new model and refined measurements of the energy spectrum and axion production.

Findings

Axion emission from scaling strings is nearly scale-invariant.

The energy spectrum of sub-horizon modes behaves as p_ax ln(kτ) with p_ax ≈ 10.

Total axion number density is approximately 1.66(17) f_a^2 H.

Abstract

Cosmic strings formed when the Peccei-Quinn symmetry breaks post-inflation are expected to emit axions throughout their lifetime. The details of the evolution of this network and the associated spectrum of axions are crucial for obtaining an accurate axion mass prediction, thus guiding searches at haloscopes. In a previous publication, we obtained evidence for the standard scaling of axion string networks, showing that the number of horizon lengths of string per horizon volume asymptotes to an $\mathcal{O}(1)$ constant. In this article, we turn our attention to the axion spectra, studying spectra of all components of the axion current and their unequal time correlators. With the new information we are better able to distinguish the contributions from propagating axions from the field carried by the strings, and show that previous measurements of the axion energy spectrum based only on the timelike component of the current are approximately 30\% derived from the string fields. We introduce a simple model based on an ensemble of string segments, which accounts for the general features of the spectra and time correlations. We conclude that axion emission from a scaling string network is close to scale-invariant ($q \approx 1$), and that the energy spectrum of sub-horizon modes behaves as $p_\text{ax}\ln( k \tau)$, where $k$ is the comoving wavenumber, $\tau$ the conformal time and $p_\text{ax} \simeq 10$. The number density spectrum evolves towards a single curve for $k\tau \lesssim 10^2$, with higher wavenumber deviations arising from initial conditions and resonant axion production at the string width scale. The total number density of axions produced from strings is $n_\text{ax}=1.66(17) f_\text{a}^2 H$, where $f_\text{a}$ is the axion decay constant and $H$ the Hubble rate. We report on axion production from the final collapse of the network in a future work.