Gravitational wave bursts from cusps and kinks on cosmic strings

The strong beams of high-frequency gravitational waves (GW) emitted by cusps and kinks of cosmic strings are studied in detail. As a consequence of these beams, the stochastic ensemble of GW's generated by a cosmological network of oscillating loops is strongly non Gaussian, and includes occasional sharp bursts that stand above the ``confusion'' GW noise made of many smaller overlapping bursts. Even if only 10% of all string loops have cusps these bursts might be detectable by the planned GW detectors LIGO/VIRGO and LISA for string tensions as small as $G \mu \sim 10^{-13}$. In the implausible case where the average cusp number per loop oscillation is extremely small, the smaller bursts emitted by the ubiquitous kinks will be detectable by LISA for string tensions as small as $G \mu \sim 10^{-12}$. We show that the strongly non Gaussian nature of the stochastic GW's generated by strings modifies the usual derivation of constraints on $G \mu$ from pulsar timing experiments. In particular the usually considered ``rms GW background'' is, when $G \mu \gaq 10^{-7}$, an overestimate of the more relevant confusion GW noise because it includes rare, intense bursts. The consideration of the confusion GW noise suggests that a Grand Unified Theory (GUT) value $ G \mu \sim 10^{-6}$ is compatible with existing pulsar data, and that a modest improvement in pulsar timing accuracy could detect the confusion noise coming from a network of cuspy string loops down to $ G \mu \sim 10^{-11}$. The GW bursts discussed here might be accompanied by Gamma Ray Bursts.