Spectrum of Primordial Gravitational Waves in Presence of a Cosmic String

In this paper we consider an inflating universe with long straight cosmic string along z-axis. We show that the effect of cosmic string can be taken as a perturbation on the background of FRW metric. Then by doing cosmological perturbations on this inflating cosmic string background, we find linearized Einstein field equations. We show that at leading order (ignoring the mixing terms of cosmic string perturbations with gravitational tensor perturbations), the cosmic string appears as an inhomogeneous term on the right hand side of wave equation of tensor perturbations . Then by finding analytical solution of the wave equation for slow-roll inflation, we show how it effects on the spectrum of primordial gravitational waves.