High-Quality Axion Dark Matter at Gravitational Wave Interferometers

Abstract

Gravitational effects are known to violate global symmetries, threatening the Peccei-Quinn (PQ) solution to the strong CP problem. Ultraviolet completions featuring a gauged $U(1)$ symmetry, where $U(1)_{\rm PQ}$ arises as an accidental global symmetry, can suppress Planck-suppressed operators, enabling high-quality axions in a mass window where it can also account for the observed dark matter (DM) in the Universe. We show that in such models, the spontaneous breaking of the $U(1)$ gauge symmetry generates a strong stochastic gravitational wave background (SGWB) from gauge cosmic string loops. For breaking scales $\gtrsim 10^{14}$ GeV, the SGWB signal strength exceeds astrophysical foregrounds across a broad frequency range. Contrary to conventional gauge cosmic string scenarios, such quality axion models have a characteristic IR break frequency originating from the collapse of string-wall network around axion oscillation temperature. We propose this characteristic SGWB frequency-amplitude region, identified as \textit{Signature-Window-Axion-Gravitational waves} (SWAG), to be a novel probe of high-quality axion DM at future space and ground-based interferometers.

Figures (3)

• Figure 1: $\bar{\theta}$ versus hierarchy of scales $f_g/f_a$, for $n = 4$ and $f_a = 3 \times 10^{11}$ GeV, which satisfies the relic abundance for axion being DM. The gray shaded region with a solid border is disfavored from current bound on neutron EDM (nEDM) Abel:2020pzs, while the shaded regions with dotted borders denote projected future sensitivities for nEDM nEDM:2019qgk and proton EDM (pEDM) Omarov:2020kws respectively. The vertical shaded region with solid border is ruled out by LIGO-O3 KAGRA:2021kbb observations while the ones with dotted borders are within reach of future GW experiments CE LIGOScientific:2016wofReitze:2019iox and ET Punturo:2010zz respectively.
• Figure 2: Left: Gravitational wave spectra (green, blue, red) for three benchmark values of $f_g / f_a$. The horizontal and vertical lines correspond to the relations defined in Eqs. \ref{['flp1']} and \ref{['fbrk']}. The dashed, dot-dashed, and dotted curves denote the LISA TD1X noise spectrum, galactic foreground, and extragalactic foregrounds, respectively. The white region overlapping with the aLIGO sensitivity represents the exclusion bound from LIGO-O3. Right: Zoomed-in view of the left panel. The region enclosed between the orange and purple lines defines the characteristic amplitude–frequency range associated with the SWAG, assuming the string network collapses at the domain wall formation temperature. The orange dashed line corresponds to a more realistic collapse time based on semi-analytic estimates. See main text for details.
• Figure 3: Axion-photon coupling $g_{a\gamma}$ versus axion mass $m_a$ for $n=4$ and $f_g/f_a =10^2$ (left) and $f_g/f_a =10^4$ (right). The Cyan colored point denotes the point where the axions, generated by vacuum misalignment, accounts for entire dark matter abundance. The yellow colored point correspond to the maxium value of axion mass consistent with observed relic of DM, if produced from topological defects. The window between these two points is identified as SWAG corresponding to the unique GW signature of our model. The colored bands along the KSVZ model-predicted $g_{a\gamma}$ correspond to current bounds on neutron nEDM Abel:2020pzs, SGWB (LIGO-O3) KAGRA:2021kbb and future sensitivities for nEDM nEDM:2019qgk, pEDM Omarov:2020kws, SGWB (CE LIGOScientific:2016wofReitze:2019iox and ET Punturo:2010zz) respectively. Other solid and dashed contours represent different bounds and future sensitivities respectively for axions, see text for details.