Revisiting the velocity-dependent one-scale model for monopoles

We revisit the physical properties of global and local monopoles and discuss their implications in the dynamics of monopole networks. In particular, we review the velocity-dependent one-scale (VOS) model for global and local monopoles and propose physically motivated changes to its equations. We suggest a new form for the acceleration term of the evolution equation of the root-mean-squared velocity and show that, with this change, the VOS model is able to describe the results of radiation and matter era numerical simulations of global monopole networks with a single value of the acceleration parameter $k$, thus resolving the tension previously found in the literature. We also show that the fact that the energy of global monopoles is not localized within their cores affects their dynamics and thus the Hubble damping terms in the VOS equations. We study the ultrarelativistic linear scaling regime predicted by the VOS equations and demonstrate that it cannot be attained either on radiation or matter eras and thus cannot arise from the cosmological evolution of a global monopole network. We also briefly discuss the implications of our findings for the VOS model for local monopoles.

Figure 1

The value of the acceleration parameter $k$ measured using the radiation (orange line) and matter (blue line) era simulations in Ref. [8] as a function of $\alpha$. The shaded areas represent the uncertainties associated with the determination of $k$ (obtained using linear propagation of the uncertainties in $\xi$ and $\overline{v}$).

Figure 2

Region of parameter space $(\beta ,\alpha )$ for which the ultrarelativistic linear scaling regime is unstable, assuming that $\theta =3$ and $\lambda =1$. The blue shaded area corresponds to the region which is excluded using the values of $k$ and $\tilde{c}$ inferred from matter-era simulations for calibration, while the pink shaded area corresponds to the additional exclusion region obtained when radiation-era simulations are used for calibration.