Effects of gravitational back reaction on small-scale structure of cosmic strings

We compute the gravitational back reaction on cosmic strings carrying kinks and show that it limits the growth of small-scale structure. A ‘‘two-scale’’ scaling solution results, with small-scale structure and loop formation scaling as ${\mathrm{\Gamma }}_{\mathit{k}}$Gμ times the horizon, where ${\mathrm{\Gamma }}_{\mathit{k}}$∼50. Kinks of all opening angles decay in a time scale τ∼l/(${\mathrm{\Gamma }}_{\mathit{k}}$Gμ), where l is the typical interkink distance. There are no more than (${\mathrm{\Gamma }}_{\mathit{k}}$Gμ${)}^{\mathrm{-}1}$ kinks per horizon length of long string. Gravitational radiation from the long strings is dominated by emission from small scales and is similar, both in frequency and amplitude, to that from loops chopped off the network.