  A cosmic string network created during an inflationary stage in the early
Universe - here defined as 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 re-enters the Hubble volume after
inflation. During the stretching regime, the production of cosmic string loops
and 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 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.
