We study numerically the existence in a false vacuum, of magnetic monopoles

which are “thin-walled”, ie, which correspond to a spherical region of

radius $R$ that is essentially trivial surrounded by a wall of thickness

$Deltall R$, hence the name thin wall, and finally an exterior region that

essentially corresponds to a pure Abelian magnetic monopole. Such monopoles

were dubbed false monopoles and can occur in non-abelian gauge theories where

the symmetry-broken vacuum is actually the false vacuum. This idea was first

proposed in cite{Kumar:2010mv}, however, their proof of the existence of false

monopoles was incorrect. Here we fill this lacuna and demonstrate numerically

the existence of thin-wall false monopoles. The decay via quantum tunnelling of

the false monopoles could be of importance to cosmological scenarios which

entertain epochs in which the universe is trapped in a symmetry-breaking false

vacuum.

## The Existence of Thin-Walled False Monopoles

We have conducted numerical studies to investigate the existence of magnetic monopoles in a false vacuum that have a “thin-walled” structure. These monopoles are characterized by a central region with a radius of R, which is essentially trivial, surrounded by a thin wall with a thickness of Δ that is much smaller than R. The exterior region corresponds to a pure Abelian magnetic monopole.

Initially proposed in a paper by Kumar et al. (2010), the concept of false monopoles in non-Abelian gauge theories suggests that the symmetry-broken vacuum is actually a false vacuum. However, the original proof of the existence of false monopoles was found to be incorrect.

### Numerical Evidence of Thin-Wall False Monopoles

In this study, we address the previous gap in research and provide numerical evidence for the existence of thin-wall false monopoles. Our investigations support the idea that these monopoles can indeed occur in certain non-Abelian gauge theories with a false vacuum.

### Potential Significance in Cosmological Scenarios

The decay of false monopoles through quantum tunneling may have important implications for cosmological scenarios. In particular, this phenomenon could be relevant during epochs where the universe is trapped in a symmetry-breaking false vacuum. Understanding the behavior of thin-wall false monopoles can contribute to our knowledge of such cosmological events.

### Roadmap for Future Research

- Further Validation: Additional numerical simulations and mathematical analyses are needed to validate our findings and confirm the existence of thin-wall false monopoles in various non-Abelian gauge theories.
- Quantum Tunneling Studies: Investigating the decay process of false monopoles through quantum tunneling is crucial for comprehending their behavior and potential cosmological consequences.
- Cosmological Applications: Explore the impact of thin-wall false monopoles on cosmological scenarios, such as inflationary models or early universe dynamics, to assess their significance in shaping the evolution of the universe.
- Extended Gauge Theories: Extend our investigations to more complex gauge theories beyond non-Abelian theories, considering the potential existence of thin-wall false monopoles in these extended frameworks.

**Challenges:**

- Complex Numerical Simulations: Numerically studying the properties and dynamics of thin-wall false monopoles requires computationally intensive simulations.
- Verification of Results: Ensuring the accuracy and reliability of numerical results through techniques like convergence tests and comparisons with other analytical or numerical approaches can be time-consuming.

**Opportunities:**

- Improved Cosmological Understanding: Gaining insights into the decay mechanisms and behavior of false monopoles can enhance our understanding of cosmological phenomena and potentially bridge gaps in current theories.
- Technological Advancements: Development of more efficient computational methods and high-performance computing infrastructure can expedite numerical investigations and facilitate larger-scale simulations.

Overall, the study of thin-wall false monopoles offers promising avenues for advancing our knowledge of non-Abelian gauge theories, the behavior of monopoles in false vacua, and their implications in cosmology. Further research and rigorous validation are essential for establishing the significance of these phenomena in broader theoretical frameworks and practical cosmological scenarios.