Multimodal axion emissions from Abelian-Higgs cosmic strings

This paper demonstrates that axion-gauge coupling enables Abelian-Higgs cosmic strings to produce multimodal axion emissions—spanning both low-energy cold dark matter and high-energy dark radiation—through string reconnection and subsequent kink dynamics, offering a viable explanation for GeV-scale axion dark matter and testable dark radiation predictions.

The Gist

The Big Picture: Cosmic "Wires" and Invisible Particles

Imagine the early universe wasn't just a smooth, expanding soup, but a place where giant, invisible "wires" stretched across space. Physicists call these cosmic strings. They are like one-dimensional cracks in the fabric of reality, formed when a fundamental symmetry of the universe broke, similar to how ice cracks when water freezes.

This paper explores what happens when these cosmic strings move, crash into each other, and reconnect. The authors discovered a new way these strings can create a mysterious particle called the axion.

The Mechanism: A Cosmic Generator

To understand how the axions are made, think of the cosmic string as a high-speed train moving through a magnetic field.

1. The Trap: Inside the core of the string, there is a trapped magnetic field. Think of this like a powerful magnet frozen inside the wire.
2. The Motion: When the string moves through space, it drags this magnetic field with it.
3. The Spark: Just as moving a magnet near a wire creates electricity (a principle you learn in high school physics), the moving string creates an electric field around itself.
4. The Collision: When two strings crash into each other and reconnect (like two rubber bands snapping together), they create a chaotic region where the electric and magnetic fields interact violently.
5. The Result: This interaction acts like a cosmic generator, shooting out axions. The paper shows that the more the strings wiggle, crash, and form sharp "kinks" (bends) after reconnecting, the more axions are produced.

The Surprise: A Two-Tone Symphony

Usually, scientists thought cosmic strings mostly produced low-energy axions (slow-moving particles). However, this study used massive supercomputer simulations to watch these strings collide. They found something surprising: the strings produce axions in two distinct "modes" or ranges, like a musical instrument playing both deep bass notes and high-pitched treble notes at the same time.

• The Low Notes (Low Energy): These are the "bass" axions. They move slowly and are heavy enough to act as Cold Dark Matter. This is the invisible "glue" that holds galaxies together. The paper suggests these low-energy axions could explain exactly how much dark matter we see in the universe today.
• The High Notes (High Energy): These are the "treble" axions. They zip around at nearly the speed of light. Because they are so fast, they act like Dark Radiation (invisible energy that doesn't clump together).

Why This Matters: Solving Two Mysteries at Once

The authors propose a scenario where the universe gets a "two-for-one deal":

1. The low-energy axions provide the missing mass (Dark Matter) needed to explain why galaxies spin the way they do.
2. The high-energy axions provide extra radiation (Dark Radiation) that changes how the universe expanded in its infancy.

The paper calculates that if the axions are heavy (about the mass of a billion protons, or "GeV" scale), this mechanism perfectly matches the amount of dark matter we observe today. At the same time, it predicts a specific amount of extra radiation that future telescopes could detect by looking at the Cosmic Microwave Background (the afterglow of the Big Bang).

The "No-Backreaction" Rule

The authors had to make a simplifying assumption to run their simulations. Imagine a windmill spinning in a storm. Usually, the wind pushes the blades, and the spinning blades push back against the wind.

In this paper, the authors assumed the axions are like a gentle breeze that doesn't push back hard enough to stop the strings from moving. They checked their math and confirmed that for the specific conditions they studied, the axions don't slow down the strings enough to change the results. This allowed them to focus purely on how the strings generate the particles.

Summary

In short, this paper uses giant computer simulations to show that cosmic strings act like cosmic generators. When they crash and reconnect, they don't just make one type of particle; they create a mix of slow, heavy particles (which could be our Dark Matter) and fast, light particles (which could be Dark Radiation). This offers a new, unified explanation for two of the biggest mysteries in cosmology.

Technical Summary

1. Problem Statement

The paper addresses the origin and production mechanisms of axions, hypothetical pseudoscalar particles motivated by the Strong CP problem and predicted by various extensions of the Standard Model (including string theory).

• Context: While axions are traditionally produced via the misalignment mechanism or the decay of global cosmic strings, the production of axions from local (Abelian-Higgs) cosmic strings has been less explored. Local strings typically lose energy via gravitational waves (GWs) rather than particle emission.
• Gap: The authors investigate whether local cosmic strings, which possess a confined magnetic field ($B$) and induce an electric field ($E$) when moving, can produce axions through the axion-gauge coupling ($\chi F_{\mu\nu}\tilde{F}^{\mu\nu}$).
• Objective: To quantify the axion production rate from Abelian-Higgs string networks, determine the energy spectrum of the emitted axions, and assess their potential to constitute Dark Matter (DM) and Dark Radiation (DR).

2. Methodology

The authors employ a combination of analytical modeling and state-of-the-art numerical lattice simulations.

• Theoretical Model:

  • They utilize the Abelian-Higgs model coupled to an axion field ($\chi$).
  • Lagrangian: Includes the Higgs field ($\Phi$), gauge field ($A_\mu$), and axion ($\chi$) with a coupling term $-\frac{g_{a\gamma'}}{4} \chi F_{\mu\nu}\tilde{F}^{\mu\nu}$.
  • Parameters: They assume the Bogomol'ny-Prasad-Sommerfeld (BPS) limit ($\lambda = 2e^2$) where aligned strings do not interact, and set the coupling $g_{a\gamma'} = v^{-1}$ for numerical convenience (where $v$ is the symmetry-breaking scale).
  • Approximation: A no-backreaction approximation is used, assuming the axion production does not significantly alter the string dynamics (validated analytically in the Appendix).

• Numerical Simulations:

  • Two-String Collision: Simulated in Minkowski space to study the fundamental mechanism. Two strings collide at a right angle with velocity $v_{str} = 0.5$.
    • Grid: $N^3 = 512^3$.
    • Focus: Axion emission during reconnection and from the resulting kinks.
  • String Network Evolution: Simulated in a radiation-dominated Friedmann-Lemaître-Robertson-Walker (FLRW) universe.
    • Grid: $N^3 = 8192^3$ (large-scale).
    • Box Size: $L = 128/v$.
    • Duration: Evolved until the lattice spacing exceeded the string width.
    • Process: Initial relaxation phase (coupling off) followed by main evolution (coupling on).

3. Key Contributions

1. Identification of a Novel Production Mechanism: The paper demonstrates that local Abelian-Higgs strings can efficiently produce axions due to the $E \cdot B \neq 0$ condition generated by string motion and reconnection, a mechanism previously unquantified for local strings.
2. Discovery of Multimodal Emission: The simulations reveal that axions are not emitted in a single energy regime but exhibit a bimodal spectrum:
   • Infrared (IR): Low-energy axions ($k \lesssim v$) from decaying loops.
   • Ultraviolet (UV): High-energy axions ($k \gtrsim 10v$) from string collisions and kinks.
3. Quantification of Cosmological Impact: The authors provide a semi-analytical framework to estimate the relic abundance of axions produced via this mechanism, linking the string network dynamics to both Cold Dark Matter (CDM) and Dark Radiation (DR).

4. Key Results

• Production Dynamics:

  • Axion emission is triggered primarily by string reconnection events, causing a burst of radiation.
  • Kinks formed after reconnection act as continuous sources of axion radiation, leading to a sustained growth in the axion number density spectrum.
  • Even before collision, a small but finite $E \cdot B$ exists due to the proximity of strings, causing pre-collision emission.

• Spectral Features (Multimodality):

  • UV Component: Dominated by collisions and kinks. The spectrum extends to high momenta ($k \sim av$), scaling roughly as $k^3$ at low $k$ due to causality, then flattening.
  • IR Component: Dominated by the decay of sub-horizon loops, similar to global string scenarios.
  • The spectrum broadens over time, with the UV peak shifting to higher $k$ as the string width scales with the expansion.

• Cosmological Abundance:

  • Dark Matter (DM): The IR axions become non-relativistic. The paper derives an abundance formula (Eq. 8) showing that GeV-mass or heavier axions produced by this mechanism can fully account for the observed relic DM density ($\Omega_{DM}h^2 \approx 0.12$).
  • Dark Radiation (DR): The UV axions remain relativistic, contributing to the effective number of neutrino species ($\Delta N_{eff}$).
  • Constraints: The model predicts a sizable $\Delta N_{eff}$ (potentially $\sim 1$) which is testable by future CMB and Large Scale Structure (LSS) observations.
  • Consistency: The scenario is consistent with current GW constraints (which limit the symmetry breaking scale $v \leq 10^{14}$ GeV) and requires axion masses $\gtrsim 1$ GeV to avoid overproduction of DM.

5. Significance

• New DM Candidate: This work establishes a viable production channel for heavy axions (GeV scale) from local strings, distinct from the standard misalignment mechanism or global string decay.
• Dual Role: It offers a unified explanation where a single string network produces both the Dark Matter (via IR axions) and Dark Radiation (via UV axions) simultaneously.
• Observational Prospects:
  • Dark Radiation: The predicted $\Delta N_{eff}$ is within the reach of future CMB experiments (e.g., CMB-S4).
  • Gamma Rays: If the axion has a GeV mass, it may decay into photons; current gamma-ray telescopes could probe the coupling strength.
  • Gravitational Waves: The introduction of a new decay channel (axion emission) for string loops may suppress the GW signal from local strings, altering the expected stochastic GW background spectrum.
• Methodological Benchmark: The use of $8192^3$ grid simulations sets a new standard for resolving the dynamics of cosmic string networks and their particle emission spectra.

In conclusion, the paper fundamentally alters the understanding of local cosmic strings, showing they are not just GW sources but potent factories for axion production, with significant implications for the composition of the universe's dark sector.