More accurate gravitational wave backgrounds from cosmic strings

Abstract

We derive a general procedure for calculating the gravitational wave background (GWB) from cosmic string loops whose typical shape evolves over time, as in gravitational backreaction. Using the results of a large-scale study of numerical gravitational backreaction on Nambu-Goto cosmic string loops, we construct GWBs of backreacted cosmic strings for a range of tensions and frequencies of cosmological interest, and compare them to current and upcoming gravitational wave detectors. The GWBs are lower than prior predictions by anywhere from a few percent to around 30\%, depending on the frequency and tension in question.

Figures (5)

• Figure 1: The dependence of evaporation fraction on normalized loop age. The individual results for 71 loops are shown as thin solid blue lines, and the average $\chi$ is shown as a dashed red line. The slope of the red line lets us find a functional form for $\Gamma(\zeta)$. Larger $\Gamma$ at earlier times means that loops evaporate more rapidly as compared to later times, where the $\chi$-$\zeta$ relationship approaches a straight line.
• Figure 2: Cosmic string gravitational wave backgrounds (solid grey lines) at various tensions $G\mu$ (indicated by adjacent grey numbers). Several current and future gravitational-wave detector power-law integrated sensitivity curves are overlaid: the NANOGrav 15yr sensitivity (green, dot-dashed); the SKA 20yr sensitivity (cyan, dotted); the LISA 4yr sensitivity (purple, dotted; upper envelope: with astrophysical foregrounds; lower envelope: without foregrounds); DECIGO (light blue, dashed); BBO (dark blue, dotted); the advanced LIGO (aLIGO) design sensitivity (brown, dot-dot-dashed); the Einstein Telescope D (ET-D) configuration (orange, dashed); and the Cosmic Explorer (CE) 40 km (red, dotted). Many cosmic string GWBs would be visible in multiple detectors simultaneously.
• Figure 3: The new method (solid red line) actually calculates how loops evolve under backreaction numerically, while the prior method (dashed blue line) used a toy model of backreaction Blanco-Pillado:2017oxo. The overall effect of using the new, more accurate method is to lower the GWB amplitude across all frequencies.
• Figure 4: The new method for calculating the string GWB produces a lower amplitude $\Omega_\text{gw}$ at all tensions and frequencies considered in comparison to the prior method. This difference, expressed as the ratio of the new to old amplitude, ranges from $0.97$ down to $0.71$, with a median of $0.83$. The difference is most pronounced just below the bump in the GWB, and least pronounced just above that bump (cf. the diagonal whitish band above, and the horizontal shift of the bump in Fig. \ref{['fig:gwb-detectors']} as $G\mu$ changes). At frequencies, high above the bump, the difference approaches a factor $\zeta_\text{max}$.
• Figure 5: Gravitational-wave backgrounds at via the new method (solid red line), and using pure cusp (dotted purple line) and pure kink (dash-dotted green line) power spectra. These methods overestimate the GWB at high frequencies, but the difference in power spectrum shapes lead to potential overlaps at mid to low frequencies.