Exact Scale-Invariant Background of Gravitational Waves from Cosmic Defects

TL;DR

It is demonstrated that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum, independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged.

Abstract

We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early Universe, are such a scaling source. We emphasise that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N^(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction.

Figures (2)

• Figure 1: ETCs from simulations, $NE^T_{\rm num}(x)$ (solid black), evaluated at $t = 64$ ($t=150$ for $N=2$). From highest to lowest, we give $N$ = 2, 3, 4, 8, 12 and 20. Lowest of all is $NE^T_{\rm th}(x)$ (dashed). For $N=4$ we also show the ETCs at $t=232$, and times in between in grey, to demonstrate the excellent scaling (for $N = 2$, due to later onset of scaling, we plot from $x \geq 1.84$). The error bars on the numerical curves give the 1$\sigma$ variation over all runs, and are barely visible.
• Figure 2: Ratio of the numerical GW amplitude $\Omega_{\rm GW}^{\rm num}$ to the large $N$ analytical calculation $\Omega_{\rm GW}^{\rm th}$ (see Table \ref{['tab:a']}) and a fit to $1.1\! + 45/N^2\!$. The error bars give the 1$\sigma$ variation over all runs.