Signature of inflation in the stochastic gravitational wave background generated by cosmic string networks

A cosmic string network created during an inflationary stage in the early Universe-defined here as an i-string network-is expected to enter a transient stretching regime during inflation, in which its characteristic length is stretched to scales much larger than the Hubble radius, before attaining a standard evolution once the network reenters the Hubble volume after inflation. During the stretching regime, the production of cosmic string loops and the consequent emission of gravitational radiation are significantly suppressed. Here, we compute the power spectrum of the stochastic gravitational wave background generated by i-string networks using the velocity-dependent one-scale model to describe the network dynamics, and we demonstrate that this regime introduces a high-frequency signature on an otherwise standard spectrum of the stochastic gravitational wave background generated by cosmic strings. We argue that, if observed by current or forthcoming experiments, this signature would provide strong evidence for i-strings and, therefore, for (primordial) inflation. We also develop a simple single-parameter algorithm for the computation of the stochastic gravitational wave background generated by i-strings from that of a standard cosmic string network, which may be useful in the determination of the observational constraints to be obtained by current and forthcoming gravitational wave experiments.