Abstract
We study the system of axion strings that forms in the early Universe if the Peccei-Quinn symmetry is restored after inflation. Using numerical simulations, we establish the existence of an asymptotic solution to which the system is attracted independently of the initial conditions. We study in detail the properties of this solution, including the average number of strings per Hubble patch, the distribution of loops and long strings, the way that different types of radiation are emitted, and the shape of the spectrum of axions produced. We find clear evidence of logarithmic violations of the scaling properties of the attractor solution. We also find that, while most of the axions are emitted with momenta of order Hubble, most of the axion energy density is contained in axions with energy of order the string core scale, at least in the parameter range available in the simulation. While such a spectrum would lead to a negligible number density of relic axions from strings when extrapolated to the physical parameter region, we show that the presence of small logarithmic corrections to the spectrum shape could completely alter such a conclusion. A detailed understanding of the evolution of the axion spectrum is therefore crucial for a reliable estimate of the relic axion abundance from strings.
Highlights
The QCD axion [1,2,3,4,5,6,7] is the simplest and most robust of the known solutions of the Standard Model (SM) Strong CP problem, and it automatically forms a component of cold dark matter (DM) [8,9,10]
We find that the radius of the axion string loop as a function of time during its initial collapse does get closer to the cosine prediction
In this paper we have studied the dynamics of the global strings that form in QCD axion models when the U(1) PQ symmetry is broken after inflation
Summary
The QCD axion [1,2,3,4,5,6,7] is the simplest and most robust of the known solutions of the Standard Model (SM) Strong CP problem, and it automatically forms a component of cold dark matter (DM) [8,9,10]. In our present work we consider the string network before the axion mass turns on An understanding of this stage of its evolution is crucial, both to calculate the relic abundance of axions produced at such times and to set the appropriate initial conditions when analysing the system once the axion mass becomes relevant. Making physically relevant predictions about the system at the time of QCD crossover requires that results from simulations are extrapolated over a vast difference in scale separations. What makes such an extrapolation not obviously hopeless is the possible existence of an attractor in the evolution, an understanding of which would allow a controlled extrapolation to be made. In appendix F we analyse whether the properties of the global strings that we simulate are converging to those of local strings
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