Evolution of Cosmic String Loops under Gravitational Backreaction

Abstract

Nambu-Goto cosmic string loops generically develop cusps, points where the string momentarily reaches the speed of light. These cusps produce strong gravitational wave bursts with a characteristic strain spectrum $\tilde{h}(ω)\propto (Gμ)\,ω^{-4/3}$, making them prime targets for gravitational wave searches, where $μ$ is the string mass per unit length. However, this picture is modified when one accounts for gravitational backreaction. Using a convenient gauge, we reformulate the Nambu-Goto equations of motion for a loop moving in its own dynamically sourced gravitational field, enabling the first continuous numerical evolution of loops under this backreaction. A key finding is that locally cusps survive backreaction. Nevertheless, the gravitational waveform calculated in this formalism is significantly modified, weakening the cusp burst and introducing a high-frequency cutoff at $f_c\propto(Gμ)^{-3/2}$. This suppression above $f_c$ reduces the expected signal-to-noise ratio in current and near-future detectors relative to unperturbed waveform predictions.