  Among all cosmological quantum-gravity or quantum-gravity-inspired scenarios,
only very few predict a blue-tilted primordial tensor spectrum. We explore five
of them and check whether they can generate a stochastic gravitational-wave
background detectable by present and future interferometers: non-local quantum
gravity, string-gas cosmology, new ekpyrotic scenario, Brandenberger-Ho
non-commutative inflation and multi-fractional spacetimes. We show that
non-local quantum gravity is unobservable, while all the other models can reach
the strain sensitivity of DECIGO but not that of LIGO-Virgo-KAGRA, LISA or
Einstein Telescope. Other quantum-gravity models with red-tilted spectra (most
loop quantum cosmologies) or with exceptionally tiny quantum corrections
(Wheeler-DeWitt quantum cosmology) are found to be non-detectable.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory