The gravitational wave landscape of cosmic string networks with varying tension

We fully classify the phenomenology of gravitational wave emission from scaling cosmic string networks with varying tension and compute the spectral indices of the resulting stochastic backgrounds. In string compactifications, periods of varying tension occur when moduli acquire a time-dependence. We present concrete examples in type IIB string theory as D3- and NS5- branes wrapping internal cycles, which become dynamical due to the effect of moduli potentials. Moreover, we use Swampland constraints to derive general bounds on the allowed time-variation of the effective string tension in FLRW backgrounds and on the resulting spectral indices.