Gravitational waves from light cosmic strings: Backgrounds and bursts with large loops

The mean spectrum and burst statistics of gravitational waves produced by a cosmological population of cosmic string loops are estimated using analytic approximations, calibrated with earlier simulations. Formulas are derived showing the dependence of observables on the string tension $G\mu$, in the regime where newly-formed loops are relatively large, not very much smaller than the horizon. Large loops form earlier, are more abundant, and generate a more intense stochastic background and more frequent bursts than assumed in earlier background estimates, enabling experiments to probe lighter cosmic strings of interest to string theory. Predictions are compared with instrument noise from current and future experiments, and with confusion noise from known astrophysical gravitational-wave sources such as stellar and massive black hole binaries. In these large-loop models, current data from millisecond pulsar timing already suggests that $G\mu$ is less than about ${10}^{-10}$, close to the minimum value where bursts might be detected by Advanced LIGO, and a typical value expected in strings from brane inflation. Because of confusion noise expected from massive black hole binaries, pulsar techniques will not be able to go below about $G\mu \approx {10}^{-11}$. LISA will be sensitive to stochastic backgrounds created by strings as light as $G\mu \approx {10}^{-15}$, at frequencies where it is limited by confusion noise of Galactic stellar populations; however, for those lightest detectable strings, bursts are rarely detectable. For $G\mu >{10}^{-11}$, the stochastic background from strings dominates the LISA noise by a large factor, and burst events may also be detectable by LISA, allowing detailed study of loop behavior. Astrophysical confusion might be low enough at 0.1 to 1 Hz to eventually reach $G\mu \approx {10}^{-20}$ with future interferometer technology.

Figure 1

Predicted gravitational-wave backgrounds from strings, and noise sources. Broad band energy density is shown in units of the critical density for $h_0=1$, as a function of frequency, for $\alpha =0.1$. Noise levels are shown for current millisecond pulsar data (MSP), and projected LISA sensitivity in maximum resolution and Sagnac modes. Confusion noise is shown for massive black hole binaries (MBHB), the summed Galactic binary population including binary white dwarfs ($\mathrm{UB}+\mathrm{WUMa}+\mathrm{GCWDB}+\mathrm{CV}$), and extragalactic populations of white dwarfs (XGCWDB) and neutron stars (XGNSB). Radiation from loop populations at high redshift (H) and present-day (P) is shown, labled by the value of $G\mu$. Dotted curves show the contributions of $z>1$ loops where they are subdominant to the P contributions. Current (MSP) sensitivity is at about $G\mu \approx {10}^{-10}$, and LISA will reach to around $G\mu \approx {10}^{-15}$.