Constraints on Cosmic Strings Using Data from the Third Advanced LIGO–Virgo Observing Run

We search for gravitational-wave signals produced by cosmic strings in the Advanced LIGO and Virgo full O3 dataset. Search results are presented for gravitational waves produced by cosmic string loop features such as cusps, kinks, and, for the first time, kink-kink collisions. A template-based search for short-duration transient signals does not yield a detection. We also use the stochastic gravitational-wave background energy density upper limits derived from the O3 data to constrain the cosmic string tension $G\mu$ as a function of the number of kinks, or the number of cusps, for two cosmic string loop distribution models. Additionally, we develop and test a third model that interpolates between these two models. Our results improve upon the previous LIGO–Virgo constraints on $G\mu$ by 1 to 2 orders of magnitude depending on the model that is tested. In particular, for the one-loop distribution model, we set the most competitive constraints to date: $G\mu \lesssim 4\times {10}^{-15}$. In the case of cosmic strings formed at the end of inflation in the context of grand unified theories, these results challenge simple inflationary models.

Figure 1

Predictions of the gravitational-wave energy density spectra using different models for the loop distribution function $n(\gamma ,z)$ and for two values of the number of kinks per loop oscillation $N_k$: 1 and 100. The string tension $G\mu$ is fixed to ${10}^{-8}$. Top left: model $\mathbf{A}$, $N_k=100$. Top right: model $\mathbf{B}$, $N_k=100$. Bottom left: model $\mathbf{C}\mathbf{\text{−}}\mathbf{1}$, $N_k=1$. Bottom right: model $\mathbf{C}\mathbf{\text{−}}\mathbf{1}$, $N_k=100$. For model $\mathbf{C}\mathbf{\text{−}}\mathbf{1}$, we use the following model parameters (see the Supplemental Material [42]): ${\chi }_{\mathrm{rad}}=0.45$, ${\chi }_{\mathrm{mat}}=0.295$, $c_{\mathrm{rad}}=0.15$, $c_{\mathrm{mat}}=0.019$; the subscripts refer to the radiation and matter eras, respectively. We also show the energy density spectra of the three different components and $2\text{−}\sigma$ power-law integrated (PI) curves [55] for the O3 isotropic stochastic search [41], and projections for the Hanford, Livingston, and Virgo network at design sensitivity, and the $\mathrm{A}+\text{detectors}$ [56].

Figure 2

Left panel: cumulative distribution of cosmic string burst candidate events produced by cusps (top), kinks (middle), and kink-kink collisions (bottom). The expected distributions from background noise are represented by $\pm 1\sigma$ shaded areas. Right panel: the detection efficiency is measured using simulated signals as a function of the signal amplitude for cusps, kinks, and kink-kink collisions. Note that the horizontal axis measures different amplitude quantities $A_i$ for the three types of signals, parameterized by the waveform frequency power law $q_i$.

Figure 3

Exclusion regions at 95% C.L. on the cosmic string parameter space $(N_k,G\mu )$ derived from the stochastic search (pink) and the burst search (turquoise). Four models are considered to describe the distribution of cosmic string loops: model $\mathbf{A}$ (top left), model $\mathbf{B}$ (top right), model $\mathbf{C}\mathbf{\text{−}}\mathbf{1}$ (bottom left), and model $\mathbf{C}\mathbf{\text{−}}\mathbf{2}$ (bottom right). Note that the stochastic result combines the data of O1, O2, and O3, while the burst search only includes O3 data. We also report limits from other experiments: pulsar timing arrays (PTA) [33, 34], cosmic microwave background (CMB) [31], and Big Bang nucleosynthesis [32]. The notch in the SGWB constraint for model $\mathbf{C}\mathbf{\text{−}}\mathbf{1}$ is explained in the Supplemental Material [42].