Numerical simulations of magnetic monopole evolution in an expanding universe

TL;DR

This work addresses whether a gas of gauge monopoles formed after inflation evolves in a way consistent with velocity-one-scale (VOS) models by simulating their dynamics in an expanding universe using a lattice SU(2) gauge-Higgs theory. The authors test different Coulomb-force modifications, finding evidence that the no-modification case (α = 0) best describes the radiation-era fixed point and that the density fraction remains constant in radiation while decaying logarithmically in the matter era, in the absence of thermal bath interactions. Their results provide a quantitative support for VOS descriptions of monopole evolution and establish a framework for future studies including thermal and domain-wall effects. The work has implications for the cosmological relic abundance of monopoles and informs constraints on their mass and density in standard cosmology.

Abstract

Magnetic monopoles are an inevitable feature of post-inflation symmetry-breaking phase transitions in grand unified theories. Analytic estimates of their density indicate that they are compatible with standard cosmology only if their mass is less than $10^{11}$ GeV. We initiate a programme of numerical studies of monopole dynamics by simulating a gas of 't Hooft-Polyakov monopoles formed by the Kibble mechanism after a phase transition. In this paper we simulate monopoles in a radiation background, but without interactions with the radiation, in order to resolve differences between analytical models. We find that during the radiation era, the monopoles find each other and annihilate efficiently enough to keep their density fraction constant, which supports the modelling of Zel'dovich and Khlopov and Preskill in the epoch when plasma interactions can be neglected. In the matter era the density fraction decreases logarithmically. Further work is needed to quantify the effect of the thermal bath, which is expected to reduce the annihilation rate at later times.

Figures (8)

• Figure 1: Comoving size of the monopoles in our simulations, relative to the lattice spacing $\mathrm{d}x=1$. For $\tau < 200$, the evolution is strongly damped. For $200 < \tau < 501$, Friedmann evolution starts, but couplings are scaled with a power of the scale factor so that the comoving monopole size can grow to its physical value. Physical evolution starts at $\tau = 501$.
• Figure 2: Mean monopole separation $\xi_N$ during the radiation era shown for different parameter choices $l_0$, plotted against conformal time $\tau$. Damping phase 0 - 200 $\tau$ shown in yellow, and growth phase 201-501 $\tau$ shown in light green. Errors obtained by averaging over the $n_\text{sim}$ simulations per parameter set.
• Figure 3: The two monopole separation estimators $\xi_N$ and $\xi_{E_V}$ plotted against conformal time $\tau$ for parameter choice $l_0 = 48$. Damping phase 0 - 200 $\tau$ shown in yellow, and growth phase 201-501 $\tau$ shown in light green. Top: radiation era. Bottom: matter era.
• Figure 4: Top: The monopole density fraction during radiation era. Bottom: Matter era, with fit on Eq. (\ref{['eq:densfrac_mat_fit']}). Dashed lines are for fits from $\tau = 612$ onwards, dotted lines for fits from $\tau = 812$ onwards. For both, only the main simulation phase is shown.
• Figure 5: Monopole velocity estimators and $d\xi_N/d\tau = \dot{\xi}$ compared during growth phase (201-501 $\tau$) and main simulation phase. Savitzky-Golay filter has been applied to $d\xi_N/d\tau$ to smooth the data. From top to bottom, $l_0 = 96, 48, 32, 16$ are shown for radiation era. Last (bottom) plot shows matter era.