Stochastic gravitational waves from cosmic string loops in scaling

If cosmic strings are formed in the early universe, their associated loops emit gravitational waves during the whole cosmic history and contribute to the stochastic gravitational wave background at all frequencies. We provide a new estimate of the stochastic gravitational wave spectrum by considering a realistic cosmological loop distribution, in scaling, as it can be inferred from Nambu-Goto numerical simulations. Our result takes into account various effects neglected so far. We include both gravitational wave emission and backreaction effects on the loop distribution and show that they produce two distinct features in the spectrum. Concerning the string microstructure, in addition to the presence of cusps and kinks, we show that gravitational wave bursts created by the collision of kinks could dominate the signal for wiggly strings, a situation which may be favoured in the light of recent numerical simulations. In view of these new results, we propose four prototypical scenarios, within the margin of the remaining theoretical uncertainties, for which we derive the corresponding signal and estimate the constraints on the string tension put by both the LIGO and European Pulsar Timing Array (EPTA) observations. The less constrained of these scenarios is shown to have a string tension GU < 7.2 x 10^{-11}, at 95% of confidence. Smooth loops carrying two cusps per oscillation verify the two-sigma bound GU < 1.0 x 10^{-11} while the most constrained of all scenarios describes very kinky loops and satisfies GU < 6.7 x 10^{-14} at 95% of confidence.