TABLE I: Various constants appearing in the calculation of kink distribution and the spectrum of GWs from kinks. We have to solve this equation under an appropriate initial condition. The initial con- dition to be imposed depends on how strings emerge. We consider two typical scenarios. As a first scenario, let us suppose that cosmic strings form when spontaneous symmetry breaking (SSB) occurs in the radiation dominated Universe. After the formation, cosmic strings interact with particles in thermal bath, which acts as friction on the string. At first this friction effect overcomes the Hubble expansion. (This epoch is called friction-dominated era.) The important observation is that the friction effect smoothens strings and washes out the small scale structure on them [14]. The temperature at which friction domination ends is given by [15] where G is the Newton constant and M$_{pl}$ is the Planck scale. If the temperature at the string formation is lower than this critical value, the friction effect can be neglected from the formation epoch to the present day, and kinks emerge at the same time as appearance of strings. As a second scenario, let us suppose that cosmic strings are generated at the end of inflation, like strings made by condensation of waterfall fields in supersymmetric hybrid inflation [16–18], and cosmic superstrings left after annihilation of the D-brane and anti D-brane in brane inflation [2, 3]. In this case, cosmic strings form in the inflaton-oscillation dominated era, which resembles the matter-dominated era. Although strings feel frictions from dilute plasma existing before the reheating completes, the effect is negligible as long as the reheating temperature after inflation T$_{r}$ is lower than ∼ GµM$_{pl}$ . In this case, kinks 6 T$_{c}$ ∼ GµM$_{pl}$, (14) definition radiation dom. matter dom. γ - 0.3 0.55 ζ - 0.09 0.2 β - 1.1 1.2 A 2 ζ − β − 0 . 92 − 0 . 8 B 4 ζ − β − 0 . 74 − 0 . 4 C ( β 8 ζ ) / [3( β 2 ζ )] 0.14 0 . 17