  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 $0<a\leq 1$, 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 $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent
with the latest Planck/BICEP/Keck Array observations. Notably, the models with
$a\neq 1$ give a smaller ratio $r\leq 10^{-3}$, 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.
