Constraints on cosmic strings using data from the first Advanced LIGO observing run

Cosmic strings are topological defects which can be formed in grand unified theory scale phase transitions in the early universe. They are also predicted to form in the context of string theory. The main mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops and the subsequent emission of gravitational waves, thus offering an experimental signature for the existence of cosmic strings. Here we report on the analysis conducted to specifically search for gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the cosmic string parameters for three recent loop distribution models. In this paper, we initially derive constraints on the string tension $G\mu$ and the intercommutation probability, using not only the burst analysis performed on the O1 data set but also results from the previously published LIGO stochastic O1 analysis, pulsar timing arrays, cosmic microwave background and big-bang nucleosynthesis experiments. We show that these data sets are complementary in that they probe gravitational waves produced by cosmic string loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter space of the three loop distribution models we consider.

Figure 1

Loop size distributions predicted by three models: $M=1$, 2, 3. For each model, the loop distribution, $\mathcal{F}(\gamma ,t(z))$, is plotted for different redshift values and fixing $G\mu$ at ${10}^{-8}$.

Figure 2

In the upper plots, the red points show the measured cumulative cusp (left-hand plot) and kink (right-hand plot) GW burst rate (using $T_{\mathrm{obs}}$ as normalization) as a function of the likelihood ratio $\mathrm{\Lambda }$. The black line shows the expected background of the search with the $\pm 1\sigma$ statistical error represented by the hatched area. In both cases, the highest-ranked event (${\mathrm{\Lambda }}_h\simeq 232$ and ${\mathrm{\Lambda }}_h\simeq 611$) is consistent with the background. The lower plots show the sensitivity of the search as a function of the cusp/kink signal amplitude. This is measured by the fraction of simulated cusp/kink events recovered with $\mathrm{\Lambda }>{\mathrm{\Lambda }}_h$. The sensitivity to cusp signals is also measured for a false-alarm rate (FAR) of $1.85\times {10}^{-6}\mathrm{Hz}$ to be compared with the sensitivity of the previous LIGO-Virgo burst search [52] (dashed lines).

Figure 3

Top: GW energy density, ${\mathrm{\Omega }}_{\mathrm{GW}}^{(M)}(f)$, from cusps and kinks predicted by the three loop distribution models. The string tension $G\mu$ has been fixed to ${10}^{-8}$. Bottom: maximum strain amplitude $h^{*}$ used for the integration in Eq. (26).

Figure 4

Top: GW energy density, ${\mathrm{\Omega }}_{\mathrm{GW}}^{(M)}(f)$, from cusps for model 1. We have separated the contributions from loops in the radiation ($z>3366$) and matter ($z<3366$) eras. Additionally, for loops in the matter era, we have separated the effect of loops produced in the matter era from the ones produced in the radiation era [Eqs. (3), (4), and (6)]. Bottom: GW energy density, ${\mathrm{\Omega }}_{\mathrm{GW}}^{(M)}(f)$, from cusps for model 3. The effect of the three loop size regimes is shown [Eqs. (13), (14), and (15)] for the matter and radiation eras.

Figure 5

GW energy density, ${\mathrm{\Omega }}_{\mathrm{GW}}^{(M)}(f)$, from cusps for models 1 and 3. The spectra have been computed at the time of photon decoupling ($z_{\mathrm{CMB}}=1100$) and at the time of nucleosynthesis ($z_{\mathrm{BBN}}=5.5\times {10}^9$).

Figure 6

95% confidence exclusion regions are shown for three loop distribution models: $M=1$ (top left), $M=2$ (top right), and $M=3$ (bottom left). Shaded regions are excluded by the latest (O1) Advanced LIGO stochastic [31] and burst (presented here) measurements. We also show the bounds from the previous LIGO-Virgo stochastic measurement (S6) [63], from the indirect BBN and CMB bounds [27, 28], and from the PTA measurement (pulsar) [29]. Also shown is the projected design sensitivity of the Advanced LIGO and Advanced Virgo experiments (design, stochastic) [64]. The excluded regions are below the respective curves.

Figure 7

GW event rate predicted by models $M=1$ (top row), $M=2$ (middle row), and $M=3$ (bottom row) and averaged over either $h$ (left column) or $z$ (right column). The string tension and the wave frequency are fixed to ${10}^{-8}$ and to 100 Hz respectively. For models 1 and 2, we separated the contributions from loops in the radiation ($z>3366$) and matter ($z<3366$) eras. Additionally, for loops in the matter era, we separated the effect of loops produced in the matter era from the ones produced in the radiation era [Eqs. (3), (4), and (6)]. For model 3, the effect of the three loop size regimes is shown [Eqs. (13), (14), and (15)].

Figure 8

GW event rate predicted by model $M=1$ for different frequencies and averaged over either $h$ (left column) or $z$ (right column).