Imprints of cosmic strings on the cosmological gravitational wave background

Abstract

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 (kc) of the comoving wave number which discriminates the metric perturbations into oscillating (k>kc) and nonoscillating (k<kc) 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 (Δτ) the Universe becomes radiation dominated. The evolution of the nonoscillatory GW modes during Δτ (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 Hz<f≲105 Hz.