Spectral Fingerprints Beyond Degeneracies in Primordial Gravitational-Wave Sources

Abstract

Stochastic gravitational-wave backgrounds from different primordial mechanisms can exhibit identical peak frequencies and amplitudes, leaving their origin degenerate. We show that this degeneracy can be broken by the broadband spectral response of the gravitational-wave source. By comparing scalar-induced and gauge-field-induced gravitational waves with the same primordial spectral profile and cosmological evolution, we isolate the imprint of the tensor-source dynamics. Although both mechanisms exhibit the same infrared scaling, they develop distinct spectral shapes near the peak and different ultraviolet asymptotes. The local spectral index $n_{\mathrm{gw}}$ and its running ${\alpha }_{\mathrm{gw}}$ further characterize this source-dependent evolution, providing a spectral fingerprint beyond the peak observables. These results show that broadband, multi-frequency observations can probe the production mechanism of a primordial gravitational-wave background even when its peak frequency and amplitude are degenerate.

5+2 pages,4 figures. This version has been submitted to the journal