  We revisit the hybrid inflation model gauged by $U(1)_{B-L}$ extension of the
Minimal Supersymmetric Standard Model (MSSM) in a no-scale background.
Considering a single predictive framework, we study inflation, leptogenesis,
gavitino cosmology, and the stochastic background of gravitational waves
produced by metastable cosmic strings. The spontaneous breaking of $U(1)_{B-L}$
at the end of inflation produces a network of metastable cosmic strings while,
the interaction between $U(1)_{B-L}$ Higgs field and the neutrinos generate
heavy Majorana masses for the right-handed neutrinos. The heavy Majorana masses
explain the tiny neutrino masses via the seesaw mechanism, a realistic scenario
for reheating and non-thermal leptogenesis. We show that a successful
non-thermal leptogenesis and a stable gravitino as a dark matter candidate can
be achieved for a wide range of reheating temperatures and $U(1)_{B-L}$
symmetry breaking scales. The possibility of realizing metastable cosmic
strings in a grand unified theory (GUT) setup is briefly discussed. We find
that a successful reheating with non-thermal leptogenesis and gravitino dark
matter restrict the allowed values of string tension to a narrow range $10^{-9}
\lesssim G\mu_{CS} \lesssim 8 \times 10^{-6}$, predicting a stochastic
gravitational-wave background that lies within the 1-$\sigma$ bounds of the
recent NANOGrav 12.5-yr data, as well as within the sensitivity bounds of
future GW experiments.
