Numerical simulations of necklaces in SU(2) gauge-Higgs field theory

Abstract: We perform the first numerical simulations of necklaces in a non-Abelian gauge theory. Necklaces are composite classical solutions which can be interpreted as monopoles trapped on strings, rather generic structures in a Grand Unified Theory. We generate necklaces from random initial conditions, modelling a phase transition in the early Universe, and study the evolution. For all cases, we find that the necklace system shows scaling behaviour similar to that of a network of ordinary cosmic strings. Furthermore, our simulations indicate that comoving distance between the monopoles or semipoles along the string asymptotes to a constant value at late times. This means that while the monopole-to-string energy density ratio decreases as the inverse of the scale factor, a horizon-size length of string has a large number of monopoles, significantly affecting the dynamics of string loops. We argue that gravitational wave bounds from millisecond pulsar timing on the string tension in the Nambu-Goto scenario are greatly relaxed.

• The paper presents numerical simulations using a lattice framework to study the scaling behavior and dynamics of cosmic necklace networks in SU(2) gauge-Higgs field theory.
• Simulations reveal a scaling regime where energy density decreases as t⁻², and uniquely show monopole separation along strings tends towards a constant comoving value.
• The study finds stable root mean square velocities of strings and monopoles around 0.5c, suggesting dynamical stability and implications for cosmological models involving such defects.

Numerical Simulations of Necklaces in SU(2) Gauge-Higgs Field Theory: A Review

The paper, titled "Numerical simulations of necklaces in SU(2) gauge-Higgs field theory," presents a detailed exploration of the dynamics of cosmic necklaces, which are composite structures combining elements of monopoles and strings in a cosmological context. The research is significant for its focus on networks of non-Abelian strings formed by the symmetry-breaking pattern SU(2)$\to Z_2$, enriched by the presence of magnetic monopoles. Such structures naturally emerge from Grand Unified Theories (GUTs), making them of substantial interest for understanding early universe cosmology.

Methodology and Simulation Framework

The authors implemented a set of numerical simulations within a lattice framework to study the evolution of these cosmic necklaces. The SU(2) model considered features two adjoint Higgs fields, allowing elegant interplay between gauge fields and scalar fields in the dynamics. The simulations were conducted in a cosmological background, variably adjusting the scale factor to examine both core growth and shrinkage scenarios, an approach that elegantly circumvents the lattice resolution issues typically encountered in such studies.

Key Findings

1. Scaling Behavior: The results robustly indicate that the necklace networks exhibit a scaling regime where the energy density of the system decreases as $t^{-2}$, akin to that observed in simpler cosmic string networks. This suggests that such networks could maintain a constant energy density fraction of the universe's total density over cosmological time scales.
2. Monopole Density: In contrast to earlier models, the simulations show that the comoving monopole separation along strings tends towards a constant value, rather than shrinking continuously or coinciding with the string width. This challenges existing models of monopole decay in string networks and suggests monopole annihilation along the string is not as prevalent as previously assumed.
3. Monopole and String Velocities: The study observes that the root mean square (RMS) velocities of strings and monopoles stabilize at approximately 0.5 of the speed of light, irrespective of string-segment separations or mass ratios. This hints at a uniform motion constraint imposed by the network dynamics.
4. Linearity and Annihilation: The apparent scarcity of monopole annihilation despite relative motion along strings showcases an intriguing dynamical stability within the necklace network, suggesting significant implications for the structure and evolution of such systems.

Implications and Future Prospects

The findings presented have profound implications for theoretical physics, particularly in the context of cosmological models involving topological defects. The constant comoving separation of monopoles adds a layer of complexity to our understanding of cosmic defect networks' evolution and their observational signatures.

This study opens pathways for further investigation, particularly regarding the discrepancy between predicted and observed monopole behavior. Future research could explore higher-resolution simulations or perturbative analyses of necklace interactions, enhancing our understanding of GUT-scale topological defects' role in the cosmic web.

Additionally, the study's results may necessitate recalibration of cosmic string and monopole-based cosmological models, particularly those predicting ultra-high energy cosmic rays and gravitational waves. Understanding the energy loss mechanisms in such networks could potentially relax existing bounds on string tensions derived from gravitational wave observations and could illuminate new facets of the gravitational landscape shaped by cosmic defect dynamics.

In conclusion, while the study paints a comprehensive picture of the state and dynamics of cosmic necklaces within SU(2) gauge-Higgs field theory, it also raises critical questions about the broader implications of such structures in cosmology. Bridging this knowledge with observational cosmology remains an exciting frontier for future theoretical and computational endeavors in the field.