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.

在所有宇宙学量子引力或量子引力启发的场景中，只有极少数能预测出蓝色倾斜的原始张量谱。我们探究了其中的五个，并检查它们是否可以生成当前和未来的干涉仪可检测到的随机引力波背景：非局部量子重力，弦气体宇宙学，新的ekpyrotic场景，Brandenberger-Ho非交换通货膨胀和多分数时空。我们显示出非局部量子引力是不可观察到的，而所有其他模型都可以达到DECIGO的应变敏感性，但不能达到LIGO-Virgo-KAGRA，LISA或爱因斯坦望远镜的应变敏感性。发现其他带有红色倾斜光谱（大多数环形量子宇宙论）或具有极小的量子校正（Wheeler-DeWitt量子宇宙论）的量子重力模型是不可检测的。