Spectrum of primordial gravitational waves in the presence of a cosmic string

In this paper we consider an inflating universe with long straight cosmic string along z-axis. We demonstrate that cosmic string's effect can be treated as a perturbation on the background of FRW metric. By performing cosmological perturbations on this inflating cosmic string background, we derived the linearized Einstein field equations. We show that at leading order (neglecting 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 for tensor perturbations. Finally, by finding analytical solution of the wave equation for slow-roll inflation, we illustrate its impact on the spectrum of primordial gravitational waves.