Scaling of cosmic string loops

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 $0.1t$, in contrast to earlier simulations which found tiny loops. We expect the expanding-universe behavior to be qualitatively similar. If this expectation is correct, then the large loop sizes have important cosmological implications. In particular, the nucleosynthesis bound then becomes $G\mu \lesssim {10}^{-7}$, much tighter than that obtained from earlier analyses.

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. 3.

Figure 5

The final production function of loops $x^{2}f(x)$ from the last time interval in Fig. 4, considering only primary loops longer than 8.4.