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We investigate gravitational-wave backgrounds (GWBs) of primordial originthat would manifest only at ultra-high frequencies, from kilohertz to 100gigahertz, and leave no signal at either LIGO, Einstein Telescope, CosmicExplorer, LISA, or pulsar-timing arrays. We focus on GWBs produced by cosmicstrings and make predictions for the GW spectra scanning over high-energy scale(beyond $10^{10}$ GeV) particle physics parameters. Signals from local stringnetworks can easily be as large as the Big Bang nucleosynthesis/cosmicmicrowave background bounds, with a characteristic strain as high as $10^{-26}$in the 10 kHz band, offering prospects to probe grand unification physics inthe $10^{14}-10^{17}$ GeV energy range. In comparison, GWB from axionic stringsis suppressed (with maximal characteristic strain $\sim 10^{-31}$) due to theearly matter era induced by the associated heavy axions. We estimate the neededreach of hypothetical futuristic GW detectors to probe such GW and, therefore,the corresponding high-energy physics processes. Beyond the information of thesymmetry-breaking scale, the high-frequency spectrum encodes the microscopicstructure of the strings through the position of the UV cutoffs associated withcusps and/or kinks, as well as potential information about friction forces onthe string. The IR slope, on the other hand, reflects the physics responsiblefor the decay of the string network. We discuss possible strategies forreconstructing the scalar potential, particularly the scalar self-coupling,from the measurement of the UV cutoff of the GW spectrum.

Ultra-high frequency primordial gravitational waves beyond the kHz: the case of cosmic strings