Gravitational Waves from Long Strings and Loops
We compute the gravitational wave spectrum produced by a global cosmic string network in the scaling regime. The spectrum naturally divides at the string correlation length into infrared and ultraviolet parts. In the infrared, we derive the spectrum analytically from the unequal-time correlator of the string stress-energy tensor within the unconnected segment model, which we generalize for the first time to string loops. The loop contribution can be comparable to that of long strings, depending on the loop evolution parameters. In the ultraviolet, where structure below the correlation length dominates the source, we develop a data-driven method that connects this correlator formalism to the instantaneous radiation power spectrum measured in existing lattice simulations. The predicted spectrum rises with frequency as $Ω_{\rm GW}\propto k$ and $k^{3}$ in the infrared, and flattens into a plateau with a mild logarithmic tilt in the ultraviolet. The turnover frequency between the two is set by the mass of the Goldstone boson, the axion. Confronting the predicted spectrum with current data and projected sensitivities, we map out current constraints and future probes in the plane of the symmetry-breaking scale~$f_a$ and the axion mass~$m_a$.