A cosmic-string network in an expanding universe evolves by losing energy to loops which in turn oscillate and emit gravitational radiation. The power radiated at a frequency corresponding to the nth fundamental mode of oscillation of the loop is characterized by a dimensionless constant $P_n$, with the total power radiated being proportional to $\gamma =\Sigma P_n$. Previously, these constants were estimated by analytic or numerical analysis in idealized situations, generally for simple loop shapes. Here, we determine these constants more realistically, for loops produced in a numerical simulation of the cosmic-string network. The resulting numerical values of the $P_n$ appear to show a linear dependence on loop size, indicating that small-scale structure on the loops is very important in determining the overall radiation power. Long-string radiation is also studied, confirming this conclusion. The power radiated by a horizon-length string increases with time, because in the current simulations the small-scale structure on the string does not yet scale relative to the horizon length. With an appropriate extrapolation one can conclude that gravitational radiation from the long-string network will provide a significant energy-loss mechanism and may occur at a rate roughly comparable to energy loss due to loop formation.

• Received 13 September 1991

DOI:https://doi.org/10.1103/PhysRevD.45.1898