Spectrum of Primordial Gravitational Waves in Presence of a Cosmic String

TL;DR

This paper investigates how a cosmic string influences the spectrum of primordial gravitational waves during inflation by treating the string as a perturbation in the inflating universe's metric.

Contribution

It provides an analytical solution showing the effect of a cosmic string on gravitational wave spectrum in a slow-roll inflationary background.

Findings

Cosmic string acts as an inhomogeneous source in gravitational wave equations.

The spectrum of primordial gravitational waves is modified by the presence of a cosmic string.

Analytical solutions demonstrate the specific impact of cosmic strings on gravitational wave modes.

Abstract

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.