ELEMENTARY PARTICLE PHYSICS

Over the last decades, cosmology has delivered a grand wealth of groundbreaking discoveries and insights into the inner workings of the universe. The understanding of the universe at very large and very small scales advanced tremendously, both by experimental work, e.g. by the measurement of the accelerated expansion of the current universe and by theoretical work, e.g. by the determination of the nature of the QCD phase transition of the early universe. Very often theoretical advances drive experimental ones, like the prediction of gravitational waves finally lead to first gravitational wave observations.

It also works the other way around just as frequently, for example when the measurement of the energy and matter content of the universe revealed that there are more things than just the visible universe. These measurements in fact revealed that the known ingredients (mostly baryonic matter) account only for about 5% of the total content, with a factor 5 more attributed to dark matter and the rest to dark energy. In turn, theory has proposed candidates for dark matter to be confirmed or ruled out by experiment. To make the experiments feasible, it is necessary to provide theoretical predictions accurate enough to be actually tested. In this study one of the most attractive dark matter candidates is studied by numerical simulations.

Many suggestions were made since the evidence was strong enough for dark matter. There are certain types of dark matter, which were already observed or the existence of which was proven. For example, MACHOs (Massive Compact Halo Objects) were confirmed through gravitational lensing. These objects have masses much smaller than the mass of a star and therefore lack the ability to fuse hydrogen to produce radiation and are invisible for us.

A type of dark matter particles whose existence is certain is the neutrino. From physics of the early universe we know that there are about 113 neutrinos of all flavors and their antiparticles in each cubic centimeter. It is invisible (dark) and obviously contribute to the mass of the universe. From neutrino oscillation experiments and cosmological calculations we know that their mass is too small to be solely responsible for the whole amount of dark matter. Another problem with them is that they were relativistic at their decoupling and could not have provided enough large scale structure to our universe.

For a long time the mostly advocated dark matter candidates were the WIMPs (Weakly Interacting Massive Particles). Based on the experimental searches it seems to be less and less likely that WIMPs are responsible for the missing mass. Today, one of the theoretically best motivated dark matter candidate is the axion. It appeared originally as an explanation of a peculiar feature of the strong interaction: while the electroweak interaction breaks CP symmetry (charge conjugation parity symmetry), the strong interaction seems to be CP symmetric within stringent experimental bounds. In particular, one can introduce a CP violating angle into QCD, the theory of the strong interaction, which a priori could be of order 1, like other angles in the standard model of particle physics, but is experimentally found to be tiny. Such a fine-tuning needs a physical mechanism providing a natural way for the smallness of the parameter.

This is exactly what Peccei and Quinn did by introducing a scalar field. It is basically a dynamical version of the possible CP breaking parameter of QCD which evolves and relaxes subject to a potential with minimum at the CP conserving value of 0. As the potential for this field is determined by QCD, one can calculate it from QCD, a well known theory within the standard model. This connection enables the computation of properties of a particle beyond the standard model, the axion, from a theory within the standard model, QCD.

The experimental searches for the axion particle have been unfruitful thus far, probably due to the fact that the value of the mass of this particle is unknown, and thus highly sensitive methods for a certain mass value can not be applied. This search would greatly benefit from an estimate of the mass of the axion, and would ensure either a quicker discovery or the falsification of the axion hypothesis.

The proposed axion particles are created in the early universe. The axion field can form “topological defects” which are long and thin strings where a lot of energy is concentrated. These strings then decay into axion particles, which form the dark matter that we (indirectly) observe today. To calculate the mass of the particle this creation method has to be understood quantitatively with good accuracy.

In this study the researchers focused on the time evolution and decay of this string network as this gives an important contribution to the axion abundance in the later epochs of the evolution of the universe. This process is highly nonlinear thus understanding requires computer simulations of simplified models of the universe where the axion network is created and then the time evolution is followed. These simulations are challenging as the energy stored in the strings is much larger than the energy stored in the axion particles, and the simulation has to describe the evolution of both energy scales.

Theoretical results suggest that the evolution of the string network follows certain simple power law behaviours (aka. “scaling laws”), depending on the dimension of space-time, and the symmetries of the underlying field theoretical description of the axion strings and particles. During the simulation this power-law behaviors were observed and their parameters measured. Such results provide important clues to the theoretical description of the defects and their scaling behavior, and for a quantitative estimation for the mass of the axion particles. In the future this study can lead to further examination of the robustness of the scaling solution, and the establishment of a correction to the scaling behavior, which can give important quantitative corrections in the axion mass.