We develop generalized no-scale supergravity models of inflation, and then study the
corresponding cosmological predictions as well as the formation of primordial black holes (PBHs)
and scalar-induced gravitational waves (SIGWs). With a new parameter 0 < a ≤ 1, the generalized
no-scale supergravity provides the continuous connections among the generic no-scale supergravity
from string theory compactifications. The resulting prediction of the CMB, spectrum index ns
,
and tensor-to-scalar ratio r can be highly consistent with the latest Planck/BICEP/Keck Array
observations. Notably, the models with a ≠ 1 give a smaller ratio r ≤ 10-3, which is
flexible even under the anticipated tighter observational constraints at the future experiments.
Additionally, these models have the potential to generate a broad-band stochastic gravitational
wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the
formation of PBHs with various mass scales, which could account for a significant portion of dark
matter relic density in the Universe.