We examine which information on the early cosmological history can be extracted from the potential measurement by third-generation gravitational-wave observatories of a stochastic gravitational wave background (SGWB) produced by cosmic strings. We consider a variety of cosmological scenarios breaking the scale-invariant properties of the spectrum, such as early long matter or kination eras, short intermediate matter and inflation periods inside a radiation era, and their specific signatures on the SGWB. This requires to go beyond the usually-assumed scaling regime, to take into account the transient effects during the change of equation of state of the universe. We compute the time evolution of the string network parameters and thus the loop-production efficiency during the transient regime, and derive the corresponding shift in the turning-point frequency. We consider the impact of particle production on the gravitational-wave emission by loops. We estimate the reach of future interferometers LISA, BBO, DECIGO, ET and CE and radio telescope SKA to probe the new physics energy scale at which the universe has experienced changes in its expansion history. We find that a given interferometer may be sensitive to very different energy scales, depending on the nature and duration of the non-standard era, and the value of the string tension. It is fascinating that by exploiting the data from different GW observatories associated with distinct frequency bands, we may be able to reconstruct the full spectrum and therefore extract the values of fundamental physics parameters.

We point out that current and planned telescopes have the potential of probing annihilating Dark Matter (DM) with a mass of O(100) TeV and beyond. As a target for such searches, we propose models where DM annihilates into lighter mediators, themselves decaying into Standard Model (SM) particles. These models allow to reliably compute the energy spectra of the SM final states, and to naturally evade the unitarity bound on the DM mass. Indeed, long-lived mediators may cause an early matter-dominated phase in the evolution of the Universe and, upon decaying, dilute the density of preexisting relics thus allowing for very large DM masses. We compute this dilution in detail and provide results in a ready-to-use form. Considering for concreteness a model of dark U (1) DM, we then study both dilution and the signals at various high energy telescopes observing γ rays, neutrinos and charged cosmic rays. This study enriches the physics case of these experiments, and opens a new observational window on heavy new physics sectors.