Tribrid Inflation, Type II Leptogenesis, and Observable Gravitational Waves in $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$

We present a concrete realization of tribrid inflation within the framework of the gauge group $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. In this model, inflation is driven by the neutral components of left-handed Higgs triplets, which also play a central role in generating the observed baryon asymmetry of the universe via non-thermal leptogenesis. Tiny neutrino masses arise naturally through a type-II seesaw mechanism, facilitated by right-handed triplet fields. Supergravity corrections, stemming from the leading-order terms in a non-minimal K\"ahler potential, are essential in bringing the predictions of the scalar spectral index $n_s$ into agreement with the latest cosmological data, including the Atacama Cosmology Telescope Data Release 6, Planck 2018, and LB-BK18. A key feature of this model is the existence of a viable parameter space that predicts potentially observable primordial gravitational waves, with a tensor-to-scalar ratio $r \lesssim 0.005$, placing it within reach of upcoming experiments.