Fractal properties and small-scale structure of cosmic string networks

We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the nontrivial fractal properties of cosmic strings, in particular, the fractal dimension and renormalized string mass per unit length, and we also study velocity correlations. We demonstrate important differences between string networks in flat (Minkowski) spacetime and the two very similar expanding cases. For high resolution matter era network simulations, we provide strong evidence that small-scale structure has converged to “scaling” on all dynamical length scales, without the need for other radiative damping mechanisms. We also discuss preliminary evidence that the dominant loop production size is also approaching scaling.

Figure 1

Time evolution of large-scale properties of cosmic string networks, for 75 PPCL matter (solid lines), radiation (dashed) and flat-spacetime (dotted) runs. In all plots the horizontal axis represents the dynamic range in conformal time. All plotted quantities are defined in the text.

Figure 2

Characteristic small-scale properties of cosmic string networks in the linear scaling regime, for 75 PPCL matter (solid lines), radiation (dashed) and flat-spacetime (dotted) runs. In all cases, the properties are measured after evolution by a dynamic range of about 3. In all plots the horizontal axis represents the logarithm of the physical length scale relative to the correlation length of the network. All plotted quantities are defined in the text.

Figure 3

The multifractal dimension (top left), renormalized mass per unit length (bottom left), overall net loop production function (top right) and net loop production function from long strings only (bottom right) for a series of 5 different matter era runs. The resolutions (in PPCL) and dynamical ranges (in conformal time) are indicated in the legend.

Figure 4

The overall net loop production function for different times in the evolution of the 75 PPCL matter era run. The dynamical range of each plot, equally spaced in terms of horizon times, are indicated in the legend.