Reheating and cosmic string production

We compute the string production rate at the end of inflation, using the string spectrum obtained in [M. Li, W. Song, Y. Song, Quantizing strings in de Sitter space, JHEP 0704 (2007) 042, hep-th/0701258] in a near-de Sitter space. Our result shows that highly excited strings are hardly produced, thus the simple slow-roll inflation alone does not offer a cosmic string production mechanism.