Spectrum of gravitational waves from long-lasting primordial sources

Abstract

We discuss long-lasting gravitational wave sources arising and operating during radiation-dominated stage. Under a set of assumptions, we establish the correspondence between cosmological evolution of a source and the resulting gravitational wave spectrum. Namely, for the source energy density ρs falling as a power law characterized by the exponent β, i.e., ρs ∝ 1/aβ , where a is the Universe scale factor, the spectrum takes the form Ωgw ∝ f 2β-8 in certain ranges of values of constant β and frequencies f. In particular, matching to the best fit power law shape of stochastic gravitational wave background discovered recently by Pulsar Timing Array collaborations, one identifies β ≈ 5. We demonstrate the correspondence with concrete examples of long-lasting sources: domain walls and cosmic strings.