Imprints of cosmic strings on the cosmological gravitational wave background

The equation which governs the temporal evolution of a gravitational wave (GW) in curved space-time can be treated as the Schrödinger equation for a particle moving in the presence of an effective potential. When GWs propagate in an expanding universe with constant effective potential, there is a critical value $(k_c)$ of the comoving wave number which discriminates the metric perturbations into oscillating $(k>k_c)$ and nonoscillating $(k<k_c)$ modes. As a consequence, if the nonoscillatory modes are outside the horizon they do not freeze out. The effective potential is reduced to a nonvanishing constant in a cosmological model which is driven by a two-component fluid, consisting of radiation (dominant) and cosmic strings (subdominant). It is known that the cosmological evolution gradually results in the scaling of a cosmic-string network and, therefore, after some time $(\Delta \tau )$ the Universe becomes radiation dominated. The evolution of the nonoscillatory GW modes during $\Delta \tau$ (while they were outside the horizon), results in the distortion of the GW power spectrum from what it is anticipated in a pure radiation model, at present-time frequencies in the range ${10}^{-16}\mathrm{Hz}<f\lesssim {10}^5\mathrm{Hz}$.

Figure 1

The stochastic GW background from inflation at frequencies within the radiation era, $f\gtrsim {10}^{-16}\mathrm{Hz}$ (dashed line), under the influence of a radiation-plus-strings stage produced by GUT-scale cosmic strings (solid line).