⚛️ phenomenology

Topics in the phenomenology of axions: the cases of cosmic strings and superradiance

This dissertation investigates two key phenomenological consequences of axions: deriving constraints on their mass and symmetry breaking scale by computing the density power spectrum of axions emitted from cosmic strings, and analyzing the gravitational wave signals generated by superradiant axion clouds around spinning black holes perturbed by binary companions.

Original authors: Antonios Kyriazis

Published 2026-08-26

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Antonios Kyriazis

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is filled with invisible matter that holds galaxies together, yet we have never seen a single particle of it. This "dark matter" makes up about a quarter of everything that exists, but its true nature remains one of the biggest mysteries in physics. For decades, scientists have proposed that this missing mass could be made of axions, a hypothetical particle originally invented to solve a different puzzle about why the laws of physics treat matter and antimatter slightly differently. If axions exist, they would be incredibly light and would behave more like a wave than a solid ball. They could have been created in the earliest moments of the universe, perhaps from the breaking of cosmic strings, which are like thin, energetic cracks in the fabric of space-time. Alternatively, they could gather around spinning black holes, forming a cloud that acts like a giant, invisible atom. Understanding how these particles move and interact is crucial, because if we can predict their behavior, we might finally find a way to detect them.

A recent doctoral dissertation by Antonios Kyriazis at the University of Florida takes a deep dive into two specific ways these axions might reveal themselves. The first part of the work focuses on the "echoes" left behind by cosmic strings. Imagine the early universe as a cooling liquid; as it solidified, it might have developed cracks or defects, much like ice forming on a pond. These defects, known as cosmic strings, would have vibrated and shed particles as they evolved. Kyriazis developed a new mathematical method to calculate exactly how the particles shed by these strings would clump together over billions of years. By treating the axions as a collection of waves moving through the expanding universe, he mapped out how their density would fluctuate across space. He then compared these theoretical patterns against real data from the cosmos, looking at the distribution of galaxies and the ancient light left over from the Big Bang. The study did not find a signal from these strings, but it successfully ruled out a wide range of possibilities for how heavy the axions could be and how strong the force of their creation was. This narrows the search, telling future astronomers exactly where not to look and refining the parameters for the next generation of telescopes.

The second half of the research explores a more dynamic scenario involving black holes. When a spinning black hole is surrounded by a cloud of axions, the cloud forms a structure similar to an atom, with the black hole as the nucleus and the axions as electrons. If another massive object, like a second black hole, orbits nearby, its gravity acts like a gentle, rhythmic tug on this cloud. This tug can cause the axions to jump between energy levels, much like an electron jumping between shells in a regular atom. Kyriazis calculated that when these jumps happen, the cloud emits a distinct ripple in space-time, known as a gravitational wave. Unlike the continuous chirp of two black holes spiraling into each other, this signal is a sharp, specific tone that lasts for a short time. The study derived the exact shape and frequency of this sound, showing that it would be audible to future space-based detectors designed to listen for these faint cosmic whispers.

The research suggests that these gravitational wave signals are most likely to be found in systems where a black hole has a very high spin and is paired with a companion of a specific size. By scanning through different combinations of black hole masses and axion properties, the study identified which systems would produce the strongest signals. It turns out that the most promising candidates are those where the companion is far enough away to disturb the cloud without immediately destroying it, and where the axions are light enough to form a large cloud but heavy enough to create a detectable frequency. The work confirms that if such a system exists, the signal would be distinct enough to be separated from the background noise of the universe.

Ultimately, this dissertation provides a clear roadmap for how to listen for axions in two very different ways. It shows that even if we cannot see these particles directly, their gravitational footprints could be imprinted on the structure of the universe or heard as a unique song from a binary black hole system. By calculating the precise patterns of these echoes and the specific frequencies of these gravitational waves, the research gives experimentalists a concrete target. While the study did not discover the axion itself, it significantly sharpened the tools needed to find it, turning a broad search into a focused hunt for the invisible building blocks of our universe.

Technical Summary: Topics in the Phenomenology of Axions: The Cases of Cosmic Strings and Superradiance

Problem Statement
This dissertation addresses two distinct phenomenological consequences of axions and axion-like particles (ALPs) in the context of cosmology and black hole physics. First, it investigates the contribution of global cosmic strings to the dark matter density. While the misalignment mechanism is a standard production channel, the decay of a network of cosmic strings also emits ultra-light bosons. A critical gap in previous literature is the lack of a first-principles calculation of the density power spectrum for axions produced specifically via cosmic string decay, particularly regarding the high-wavenumber tail of the spectrum and the effects of temperature-dependent boson masses. Second, the work examines the gravitational wave (GW) phenomenology of "gravitational atoms" (GAs)—bound states of a light boson cloud around a spinning black hole—when perturbed by a companion in a binary system. While previous studies focused on the back-reaction of these systems on the binary's inspiral (e.g., orbital floating or sinking), this work seeks to derive the direct GW signal emitted by the GA itself during tidally induced resonant transitions between energy states.

Methodology

Cosmic Strings (Chapter 2):
The author models the ultralight dark matter field as a superposition of classical plane waves satisfying the Klein-Gordon equation in an expanding universe. By treating the axion field as a Gaussian random field, the work derives the two-point correlation function and subsequently the density-density correlations.
- Scaling Regime: The energy spectrum of particles emitted by the string network is parameterized based on the "scaling regime," where the number of strings per Hubble volume is constant. The spectrum is modeled as a power law with a spectral index $q$ and an infrared (IR) cutoff determined by the horizon size at the time of network collapse.
- Power Spectrum Derivation: The matter power spectrum is calculated by integrating the energy spectrum over wavenumbers, accounting for the transition from relativistic to non-relativistic evolution. The work distinguishes between temperature-independent masses (QCD axions) and temperature-dependent masses ( $m \propto T^{-n}$ ).
- Constraints: A Gaussian likelihood analysis is performed comparing the derived isocurvature power spectrum against observational data from Planck 2018, Lyman- $\alpha$ forest, UV luminosity functions (UVLF), and SDSS DR7.
Superradiance and Gravitational Atoms (Chapter 3):
The work analyzes a GA in a binary system where the companion's tidal field induces resonant transitions between superradiant states (specifically hyperfine and fine transitions).
- Hamiltonian Formulation: The system is modeled as a two-state quantum system driven by a periodic external potential (the tidal field). The Hamiltonian is transformed into a "dressed frame" to eliminate fast oscillations, reducing the problem to a Landau-Zener transition.
- Decay Rates: The analysis explicitly includes the decay rate of the final state due to black hole absorption, a factor often neglected in simplified treatments.
- GW Emission: Using the quadrupole formula, the author derives the analytical expressions for the GW strain waveform and frequency spectrum generated by the time-varying quadrupole moment of the cloud during the transition.
- Detectability: The Signal-to-Noise Ratio (SNR) is estimated for future space-based observatories (DECIGO and LISA) across a range of black hole masses, mass ratios, and boson masses.

Key Contributions and Results

Cosmic String Power Spectrum:
- The dissertation derives the isocurvature power spectrum $P_{iso}(k)$ for axions from cosmic strings from first principles, extending previous models that assumed a white-noise plateau.
- It identifies a characteristic scale $k_\star$ (related to the IR cutoff) above which the transfer function falls off, encoding information about the production mechanism. Specifically, the power spectrum exhibits a scaling of $k^{-3}$ for $k > k_\star$ , distinguishing it from the white noise plateau at lower wavenumbers.
- The work provides analytic approximations for the transfer function $T(k)$ and validates them against numerical integrations.
- Constraints: New constraints are placed on the axion mass ( $m_a$ ) and symmetry breaking scale ( $f_a$ ) using the high-wavenumber tail of the power spectrum. The analysis shows that including the tail ( $k > k_\star$ ) allows for constraints over a wider mass range than previous studies that relied solely on the white-noise plateau. Future CMB-HD lensing surveys are projected to probe $f_a$ down to $\sim 4 \times 10^{14}$ GeV for specific mass ranges.
Gravitational Wave Transitions:
- The author derives the analytical formulae for the GW strain and frequency spectrum resulting from tidally perturbed transitions in a GA. The signal is characterized as a monochromatic burst with a frequency determined by the energy splitting of the states.
- The study quantifies the impact of the final state's decay rate ( $\Gamma$ ) on the transition dynamics, showing that for small mass ratios, the decay can significantly suppress the transition probability and modify the waveform.
- Detectability: The work maps the parameter space (black hole mass, mass ratio, boson mass) to determine which systems yield the highest SNR. It identifies that hyperfine and fine transitions occur at orbital frequencies in the mHz to deci-Hz range, making them prime targets for DECIGO and LISA. The results suggest that for specific parameter choices (e.g., high spin black holes and intermediate mass ratios), these transition signals could be detectable, offering a distinct signature from standard inspiral or annihilation signals.

Significance and Claims
The dissertation claims to provide a rigorous, first-principles framework for calculating the cosmological imprints of axions produced by cosmic strings, moving beyond simplified assumptions about the power spectrum's shape. By utilizing the high-wavenumber tail of the spectrum, it extends the reach of cosmological constraints on the axion parameter space.

Regarding superradiance, the work highlights a novel GW signal channel: the direct emission from the GA during a tidal transition. While much of the literature focuses on the GA's effect on the binary's orbit, this dissertation argues that the GWs emitted by the cloud itself constitute a distinct, potentially detectable signal. The derivation of the waveform and spectrum provides the necessary tools for future searches in space-based GW observatories. The author modestly notes that the validity of the non-relativistic approximation for the cloud's wavefunction is restricted to $\alpha \lesssim 0.3$ , and relativistic corrections are required for larger coupling constants, a regime where the current analytical results serve as a baseline for future numerical computations.

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