String Decomposition and Gravitational Waves in High-quality Axion Gauge Theories

Abstract

The QCD axion can successfully solve the strong CP problem under the condition that the Peccei-Quinn symmetry is respected to extremely high standard. We explore a class of gauge theories that accommodate a high-quality axion, known as the Barr-Seckel models, paying special attention to the cosmology of topological defects. In models with domain wall number equal to unity, we show that axion strings with winding number larger than one can always be decomposed into a number of unit-winding axion strings and pure gauge strings. This mechanism enables the axion string-wall network to be destroyed timely to render a viable cosmology. The subsequent decay of gauge strings into gravitational waves generically produces a double-plateau in frequency space allowing the mechanism to be tested by upcoming experiments.

Figures (2)

• Figure 1: Schematic plot of axion string decomposition triggered by domain walls. As a concrete case, it corresponds to the first row of table \ref{['tab1']}, where a string has axion winding number $w_a=3$ in a Barr-Seckel model with $p=3, q=7$. Left panel: when the QCD potential turns on, the string is originally the junction of three axion domain walls. Right panel: around time $t_2$, the string decays following the rule presented in Eq. \ref{['eq:decomposition']}, into three unit-winding axion strings, each serving as the edge of one domain wall, plus one pure gauge string (red). After the collapsing away of the axion-string-wall system, the gauge string is left over to produce gravitational waves.
• Figure 2: Colourful curves show gravitational waves spectrum from gauge string radiation with two plateaus as a generic prediction of the Barr-Seckel models for high-quality axion. We scan the two decay constants $f_S, f_T$ in the window between $10^9$ and $10^{16}$ GeV, while keeping $f_T<f_S<10^5 f_T$ so that all axion strings and domain walls are destroyed before BBN (see Eq. \ref{['eq:t2']}). We show the sensitivity curves of future GW interferometers, pulsar time arrays, magnetic Weber bar, as well as cosmological probes of extra radiation ($\Delta N_{\rm eff}$). The grey region is excluded by the existing limit $\Delta N_{\rm eff}\lesssim0.3$Planck:2018vyg.