Scaling of cosmic string loops

Abstract

We study the spectrum of loops as a part of a complete network of cosmic strings in flat spacetime. After a long transient regime, characterized by production of small loops at the scale of the initial conditions, it appears that a true scaling regime takes over. In this final regime the characteristic length of loops scales as $0.1 t$, in contrast to earlier simulations which found tiny loops. We expect the expanding-universe behavior to be qualitatively similar. The large loop sizes have important cosmological implications. In particular, the nucleosynthesis bound becomes $Gμ\lesssim 10^{-7}$, much tighter than before.

Figures (5)

• Figure 1: A $150^3$ section of the network at time 800. Loops of sizes less than 10 are not shown.
• Figure 2: Evolution of the power spectrum $P(kt)$ vs. $kt$ at times: 60, 100, 160, 250, 400, 600, 900 (bold). Error bars are the one sigma run-to-run variation.
• Figure 3: The primary loops production function $x^2 f_p(x)$ in equal logarithmic bins of time centered at times 64, 89, 125, 175, 245, 342, 479, 671, and 939 (bold).
• Figure 4: The final production function of loops $x^2 f(x)$ for the same time intervals as Fig. \ref{['fig:primary']}.
• Figure 5: The final production function of loops $x^2 f(x)$ from the last time interval in Fig. \ref{['fig:final']}, considering only primary loops longer than $8.4$.