Whispers of Supergravity in Gravitational Wave Backgrounds: Determining the Gravitino Mass from Cosmic Thermal History

Abstract

Gravitino masses above the electroweak scale provide the simplest solution to the gravitino problem, but such large mass scales lie far beyond the reach of collider experiments. We show that the stochastic gravitational wave background offers a direct probe of this otherwise inaccessible regime. Despite decaying before Big-Bang Nucleosynthesis (BBN), these gravitinos naturally generate a period of early matter domination in the early universe. This non-standard epoch leaves a characteristic imprint on any primordial gravitational wave background, characterised by two frequencies corresponding to the onset and end of this phase. We demonstrate that these features can be used to directly infer both the gravitino mass and its initial abundance in a direct mapping. Future gravitational wave observatories span a vast frequency range, enabling sensitivity to gravitino masses from the BBN bound of $\mathcal{O}(100)\,\text{TeV}$ all the way up to $\mathcal{O}(10^{10})\,\text{TeV}$, with recent signal by NANOGrav already probing masses in the range $500$-$10^4$ TeV. Gravitational wave observables therefore probe an enormous region of parameter space, far beyond the reach of collider experiments. We are entering an era in which supergravity can be probed through gravitational wave backgrounds alongside collider experiments.