BSM with Cosmic Strings: Heavy, up to EeV mass, Unstable Particles

Unstable heavy particles well above the TeV scale are unaccessible experimentally. So far, Big-Bang Nucleosynthesis (BBN) provides the strongest limits on their mass and lifetime, the latter being shorter than 0.1 second. We show how these constraints could be potentially tremendously improved by the next generation of Gravitational-Wave (GW) interferometers, extending to lifetimes as short as $10^{-16}$ second. The key point is that these particles may have dominated the energy density of the universe and have triggered a period of matter domination at early times, until their decay before BBN. The resulting modified cosmological history compared to the usually-assumed single radiation era would imprint observable signatures in stochastic gravitational-wave backgrounds of primordial origin. In particular, we show how the detection of the GW spectrum produced by long-lasting sources such as cosmic strings would provide a unique probe of particle physics parameters. When applied to specific particle production mechanisms in the early universe, these GW spectra could be used to derive new constraints on many UV extensions of the Standard Model. We illustrate this on a few examples, such as supersymmetric models where the mass scale of scalar moduli and gravitino can be constrained up to $10^{10}$ GeV. Further bounds can be obtained on the reheating temperature of models with only-gravitationally-interacting particles as well as on the kinetic mixing of heavy dark photons at the level of $10^{-18}$.