't Hooft-Polyakovin monopolit varhaisessa maailmankaikkeudessa

The purpose of this work is to investigate the scaling of ’t Hooft-Polyakov monopoles in the early universe. These monopoles are a general prediction of a grand unified theory phase transition in the early universe. Understanding the behavior of monopoles in the early universe is thus important. We tentatively find a scaling for monopole separation which predicts that the fraction of the universe’s energy in monopoles remains constant in the radiation era, regardless of initial monopole density. We perform lattice simulations on an expanding lattice with a cosmological background. We use the simplest fields which produce ’t Hooft-Polyakov monopoles, namely the SU(2) gauge fields and a Higgs field in the adjoint representation. We initialize the fields such that we can control the initial monopole density. At the beginning of the simulations, a damping phase is performed to suppress nonphysical fluctuations in the fields, which are remnants from the initialization. The fields are then evolved according to the discretized field equations. Among other things, the number of monopoles is counted periodically during the simulation. To extend the dynamical range of the runs, the Press-Spergel-Ryden method is used to first grow the monopole size before the main evolution phase. There are different ways to estimate the average separation between monopoles in a monopole network, as well as to estimate the root mean square velocity of the monopoles. We use these estimators to find out how the average separation and velocity evolve during the runs. To find the scaling solution of the system, we fit the separation estimate on a function of conformal time. This way we find that the average separation ξ depends on conformal time η as ξ ∝ η^(1/3) , which indicates that the monopole density scales in conformal time the same way as the critical energy density of the universe. We additionally find that the velocity measured with the velocity estimators depends on the separation as approximately v ∝ dξ/dη. It’s been shown that a possible grand unified phase transition would produce an abundance of ’t Hooft-Polyakov monopoles and that some of these would survive to the present day and begin to dominate the energy density of the universe. Our result seemingly disagrees with this prediction, though there are several reasons why the predictions might not be compatible with the model we simulate. For one, in our model the monopoles do not move with thermal velocities, unlike what most of the predictions assume happens in the early universe. Thus future work of simulations with thermal velocities added would be needed. Additionally we ran simulations only in the radiation dominated era of the universe. During the matter domination era, the monopoles might behave differently