Numerical gravitational backreaction on cosmic string loops from simulation

TL;DR

The paper tackles how gravitational backreaction alters cosmic string loops derived from network simulations. It introduces a numerical framework that evolves piecewise-linear Nambu-Goto strings under linearized gravity, tracking how backreaction smooths small-scale structure, modifies the gravitational-wave power spectrum, and occasionally induces self-intersections, while showing cusps remain weak and subdominant to total emission. The main contributions are a detailed characterization of loop smoothing, cusp weakness, and the evolution of the GW-related quantity $\Gamma$ as loops evaporate (characterized by $\chi$), together with efficient methods to compute high-$n$ GW power spectra. These results refine predictions for the stochastic gravitational-wave background and burst signals from cosmic strings and provide a pathway to extrapolate simulations to real cosmological loops; a companion paper will address broader implications for GW observables.

Abstract

We report on the results of performing computational gravitational backreaction on cosmic string loops taken from a network simulation. The principal effect of backreaction is to smooth out small-scale structure on loops, which we demonstrate by various measures including the average loop power spectrum and the distribution of kink angles on the loops. Backreaction does lead to self-intersections in most cases, but these are typically small. An important effect discussed in prior work is the rounding off of kinks to form cusps, but we find that the cusps produced by that process are very weak and do not significantly contribute to the total gravitational-wave radiation of the loop. We comment briefly on extrapolating our results to loops as they would be found in nature.

Figures (11)

• Figure 1: The distribution of segment count for the 198 loops we evolve under gravitational backreaction. All loops were produced in the radiation era in the conformal time range $\tau=250\ldots400$.
• Figure 2: To faithfully represent the rounding-off of a kink by backreaction, more points are needed on one side of the kink. The blue lines represent segments of a string with a kink prior to backreaction; the red lines represent those same segments after backreaction. The segments "below" the kink---in the direction of kink motion---experience more length loss and bending due to backreaction, and thus all nine segments are necessary to capture the evolution, but "above" the kink could be faithfully represented with fewer points.
• Figure 3: An example of how backreaction changes a loop for a single member of our corpus shown at 0% evaporation and 50% evaporation. This comparison is done at corresponding points in the oscillation period; bluer segments are those more slowly moving at that instant, and redder segments more quickly. The unevaporated loop has a more jagged structure, both in the sense of directional variation along the loop and in the sense of changing speed from segment to segment. The evaporated loop retains the general rectangular shape, with four large kinks, but both the directional and speed variations have been smoothed out by backreaction. This loop stays in a non-self-intersecting trajectory throughout the entire process of backreaction, so the number of kinks stays constant during its evaporation.
• Figure 4: Distributions of various measures of intersections due to gravitational backreaction for the 70%-evaporated sub-population. While intersections are generic, they are generally small in terms of the length lost as well as their effect on the motion of the loop. While intersections become more common with increased evaporation fraction, there is no correlation between $\chi$ and the amount of length lost to intersection.
• Figure 5: The change to the average power spectrum, $P_n$, with evaporation fraction for the 70%-evaporated subpopulation with all loops given equal weight. The shape of the spectrum at low mode numbers, representing the large-scale structure of the loop, is not greatly changed. The significant change at moderate mode numbers is due to the smoothing of small-scale structure. The reduced amplitude of the bump indicates that the typical size of a change in the string direction is decreasing, and the reduced value of $n$ for this peak indicates that the length scale on which we expect a change in direction is increasing.