Cosmic Walls of Dark Matter: New Insights into Axion Dynamics

Author: Denis Avetisyan

A new theoretical study explores the behavior of axion domain walls in the early universe, revealing how plasma interactions and thermal effects shape these potential dark matter candidates.

The study demonstrates that the rescaled root-mean-square velocity of an axion domain wall network evolves predictably with conformal time, indicating a parameter space-where the axion mass <span class="katex-eq" data-katex-display="false">m_a \lesssim 10^8 \text{ eV}</span> and the coupling <span class="katex-eq" data-katex-display="false">g_{a\gamma\gamma}</span> are relatively small-distinct from previously explored, friction-dominated regimes, as evidenced by concurrent tracking of the rescaled energy density. — The study demonstrates that the rescaled root-mean-square velocity of an axion domain wall network evolves predictably with conformal time, indicating a parameter space-where the axion mass $m_a \lesssim 10^8 \text{ eV}$ and the coupling $g_{a\gamma\gamma}$ are relatively small-distinct from previously explored, friction-dominated regimes, as evidenced by concurrent tracking of the rescaled energy density.

nullquilibrium quantum field theory calculations demonstrate the significant role of thermal friction in the evolution of axion domain walls.

Predicting the abundance of dark matter from axions remains challenging due to uncertainties in modeling the complex dynamics of topological defects. This paper, ‘Axion domain walls and thermal friction’, presents a novel analytical framework-based on nonequilibrium quantum field theory-to investigate the evolution of axion domain wall networks in the early universe. Our approach reveals the significant impact of thermal and plasma effects on domain wall dynamics, potentially refining cosmological estimates of axion dark matter. Could a more accurate understanding of these effects unlock new insights into the nature of dark matter and the fundamental symmetries of the universe?

The Universe’s Fine-Tuning: A Persistent Enigma

The universe appears remarkably fine-tuned; a slight deviation in the strong force’s behavior, described by a parameter called the θ (theta) angle, would violate observed symmetries and predict an electric dipole moment for the neutron – a phenomenon never detected. This discrepancy, known as the strong CP problem, isn’t a matter of experimental error, but a deep theoretical puzzle that has vexed particle physicists for decades. The problem arises from the Standard Model of particle physics, which allows for this CP violation, yet observations suggest it should be vanishingly small. Consequently, physicists have long sought an explanation that dynamically forces the θ angle to zero, or equivalently, introduces a mechanism to cancel out the problematic term. The persistence of this mystery underscores a fundamental gap in understanding the strong force and motivates the search for physics beyond the Standard Model, making a compelling solution not merely desirable, but essential for a complete picture of the universe.

The Peccei-Quinn mechanism proposes a clever solution to the strong CP problem by introducing a new symmetry into the Standard Model of particle physics. This symmetry, when spontaneously broken, gives rise to a neutral particle known as the axion. Unlike many hypothetical particles, the axion isn’t simply predicted – its properties are largely determined by the need to resolve the strong CP problem, resulting in a remarkably constrained mass range and incredibly weak interactions. These weak interactions mean axions would barely register with normal matter, making them elusive but also ideal dark matter candidates. Furthermore, the mechanism predicts that axions possess a unique property called “flavor-changing neutral currents,” potentially allowing for their detection through the conversion of photons into axions in the presence of strong magnetic fields – a cornerstone of many current axion search experiments.

The axion’s appeal extends beyond its elegant resolution of the strong CP problem; it simultaneously presents a compelling dark matter candidate, fueling a surge in experimental investigations. Cosmological observations indicate that approximately 85

Domain Walls and the Echoes of Symmetry Breaking

Axion fields, postulated as solutions to the strong CP problem in quantum chromodynamics, exhibit a naturally occurring phenomenon of domain wall formation during the early universe. This arises from the spontaneous breaking of a global U(1) symmetry associated with the axion field. As the universe cooled, different regions settled into different vacuum states of the axion field, demarcated by domain walls – topological defects representing boundaries between these regions. The density and configuration of these domain walls are determined by the specifics of the symmetry breaking and the initial conditions in the early universe. These walls are not merely spatial boundaries; they possess energy density and can interact, forming a complex network that evolves over time, potentially influencing cosmological parameters.

The QCD Crossover, occurring at a temperature of approximately 150-160 MeV, represents the transition of Quantum Chromodynamics (QCD) from a plasma of deconfined quarks and gluons to a state of confined hadrons. This phase transition is directly related to the formation of domain walls associated with axion fields because the axion acquires a mass term at this point. Prior to the QCD Crossover, the axion field is massless, allowing for degenerate vacuum states and the subsequent creation of domain walls where different vacua meet. As the universe cooled and the QCD Crossover occurred, the axion gained a mass, ‘freezing’ the orientation of the axion field in different regions of space and solidifying these boundaries – the domain walls – which then define regions of differing axion field orientation.

The energy density contributed by domain wall networks is a crucial cosmological consideration. Domain walls, defects in spacetime, possess a surface tension that scales with the symmetry breaking scale Λ. Consequently, the energy density scales as $\Lambda^2 / L$ , where $L$ represents the typical separation between domain walls. If $L$ is not sufficiently large, the domain wall network can dominate the energy density of the early universe, potentially leading to a closed universe or conflicting with observations of the cosmic microwave background. Therefore, accurate modeling of domain wall annihilation and evolution is essential for determining their cosmological impact and constraining parameters of beyond-the-Standard-Model physics, such as the axion mass.

Modeling Axion Dynamics: A Real-Time Quantum Approach

The Schwinger-Keldysh formalism, also known as “real-time” quantum field theory, is utilized to analyze the non-equilibrium dynamics of the axion domain wall network. Unlike standard equilibrium quantum field theory which assumes thermal equilibrium, this formalism propagates fields forward and backward in time, represented by a doubled set of fields. This approach allows for the consistent treatment of time-dependent backgrounds, crucial for modeling the expanding universe and the evolving domain wall network. The formalism inherently incorporates both the forward- and backward-propagating components of quantum fields, enabling the calculation of time-ordered correlation functions and providing a framework to study processes far from thermal equilibrium, such as domain wall annihilation and the generation of non-thermal axion radiation. This is achieved through the introduction of a closed time-like contour, effectively tracing the field’s evolution in both forward and reverse time.

The Effective Action, central to describing axion dynamics in cosmology, is constructed utilizing the Friedmann-Lemaître-Robertson-Walker (FLRW) metric to account for the expanding universe. This action, a functional of the axion field, incorporates terms representing the kinetic and potential energy of the axion, as well as interactions with background gravitational fields. Specifically, the FLRW metric, expressed as $ds^2 = -dt^2 + a(t)^2 d\vec{x}^2$ , dictates the spacetime geometry and influences the propagation and evolution of axion perturbations. Consequently, the Effective Action allows for the calculation of quantities such as the power spectrum of density fluctuations and the energy density of the axion field, providing a means to model the axion’s role in the early universe and its potential contribution to dark matter.

The Two-Particle-Irreducible (2PI) Effective Action builds upon the Schwinger-Keldysh formalism to provide a means of calculating the time evolution of the axion domain wall network. This approach facilitates the derivation of coupled equations governing the network’s dynamics, specifically addressing scenarios where the axion mass is greater than or equal to $10^8$ eV. By systematically including loop corrections and self-energies, the 2PI formalism allows for the investigation of strong-field effects and the exploration of parameter spaces inaccessible to simpler perturbative treatments. The resulting equations account for both the creation and annihilation of domain walls, enabling a quantitative assessment of the network’s density and energy distribution as a function of cosmological time.

Simulating the Network: Statistical Approaches and Validation

The Fokker-Planck equation provides a probabilistic description of the domain wall network’s evolution by tracking the distribution of domain walls based on their energy density and root-mean-square (RMS) velocity. This approach treats the network not as a collection of discrete walls, but as a continuous density function in phase space defined by these two key parameters. The equation accounts for diffusive and drag forces acting on the walls, arising from interactions with the thermal plasma and internal network tension, allowing for the calculation of how the distribution of walls changes over time. Specifically, the time evolution of the distribution function $P(E, v)$ , where $E$ represents energy density and $v$ is the RMS velocity, is governed by a partial differential equation that includes terms representing diffusion in both energy and velocity space, as well as a drag term proportional to the velocity. This methodology allows for predictions of network behavior, such as the decay of energy density and the evolution of the velocity distribution, without explicitly simulating individual domain walls.

Collision integrals are incorporated into the Fokker-Planck description to account for interactions that alter the statistical properties of the domain wall network. These integrals quantify the rate of change in the distribution function due to collisions between domain walls themselves, as well as interactions with particles in the surrounding thermal plasma. Specifically, the integrals model the effects of wall annihilations, reconnections, and drag forces exerted by the plasma, all of which contribute to energy dissipation and changes in the network’s overall velocity. Accurate representation of these collision terms is crucial for simulating realistic network evolution and obtaining reliable predictions about its behavior, particularly regarding energy transfer between the network and the plasma.

VOS models, derived from the Fokker-Planck description, utilize an analytical approach to approximate the evolution of domain wall networks by focusing on statistical properties rather than tracking individual wall movements. These models typically express network dynamics through equations governing quantities like the average domain wall length and the RMS velocity of walls, allowing for predictions of network behavior under varying conditions. Importantly, VOS models serve as a critical benchmark for numerical simulations; by comparing simulation outputs to analytical VOS predictions, researchers can validate the accuracy and identify potential limitations of their simulation methodologies and parameter choices. Discrepancies between simulation results and VOS model predictions often indicate the need for refinements in the simulation’s treatment of physical processes or boundary conditions.

Beyond the Standard Model: The Axiverse and Future Exploration

Recent advancements in theoretical and computational physics are pointing toward a landscape far richer than previously imagined, hinting at the existence of an ‘axiverse’ – a vast collection of axion-like particles (ALPs). These ALPs, while sharing some characteristics with the original axion proposed to solve the strong CP problem, possess a diverse range of masses and interaction strengths. The successful modeling of axion behavior, utilizing sophisticated numerical techniques, suggests that this isn’t a singular particle but rather a whole family of them, potentially interacting with both standard model particles and dark matter. This expanded axiverse offers compelling explanations for several cosmological puzzles, including dark matter composition and the observed abundance of ultra-high-energy cosmic rays, and motivates a broadened search for these elusive particles through dedicated experimental programs.

The search for axion-like particles (ALPs) represents a compelling frontier in modern physics, offering potential solutions to problems that lie beyond the reach of the Standard Model. These hypothetical particles, predicted by extensions to the Standard Model, could account for the nature of dark matter, a substance comprising approximately 85

Recent investigations have revealed the significant role of thermal friction in shaping the dynamics of domain wall velocities and the subsequent evolution of energy density within axion-like particle systems. This detailed understanding of frictional forces-which oppose the motion of these walls-provides a crucial foundation for interpreting the results of ongoing and future experimental searches. By accurately modeling these effects, researchers can refine predictions regarding the detectability of axions and related particles, bridging the gap between theoretical frameworks and observational data. This work not only enhances the precision of simulations but also offers a pathway to disentangle genuine signals from background noise, ultimately accelerating the exploration of physics beyond the Standard Model and potentially illuminating the nature of dark matter.

The study meticulously charts the behavior of axion domain walls, acknowledging the inherent complexities of early universe cosmology. It doesn’t presume a definitive answer, instead focusing on how thermal and plasma effects change the predicted evolution of these structures. This approach echoes a fundamental principle of scientific inquiry: truth isn’t found in unwavering certainty, but in the rigorous testing of assumptions. As Carl Sagan once observed, ‘Somewhere, something incredible is waiting to be known.’ This research doesn’t claim to have that knowledge, but it meticulously refines the models used to search for it, recognizing that every dataset is merely an opinion from reality, subject to constant revision and refinement. The focus on nonequilibrium dynamics acknowledges the messy, imperfect nature of the universe and the limitations of idealized simulations.

Where Do We Go From Here?

The treatment of axion domain walls, as presented, offers a refinement-not a resolution-of a persistent problem. The calculations demonstrate the expected sensitivity to thermal and plasma effects, which is hardly surprising; a model, after all, is only as robust as its assumptions about the ambient conditions. What remains elusive is not merely a precise determination of domain wall annihilation rates, but a compelling link to observable phenomena. To claim a definitive signature requires exceeding the current capacity to disentangle these effects from the broader tapestry of early universe processes-a task where statistical significance often proves a frustratingly distant goal.

Future work will undoubtedly focus on more sophisticated treatments of backreaction. The approximations employed here, while necessary, represent a tacit admission of incomplete understanding. A fully kinetic treatment, while computationally demanding, might reveal subtle instabilities or decay channels currently obscured. More provocatively, one wonders if the emphasis on domain walls-these topological defects inherited from a broken symmetry-is itself a fruitful avenue. Perhaps the true insight lies not in their ultimate fate, but in the implications of their existence for the fundamental parameters governing the Peccei-Quinn symmetry itself.

Ultimately, the pursuit of axion dark matter-and the domain walls it may spawn-is an exercise in iterative refinement. Each calculation narrows the parameter space, each simulation exposes a new approximation. The signal, if it exists, will not announce itself with fanfare; it will emerge, slowly, from the noise-a testament not to brilliance, but to the relentless application of skepticism.

Original article: https://arxiv.org/pdf/2512.23775.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/