Smooth $\mu$-Hybrid and Non-Minimal Higgs Inflation in $SU(4)_{C}\times SU(2)_{L}\times SU(2)_{R}$ With Observable Gravitational Waves

We propose to study a smooth variant of the $\mu$-hybrid inflation model and a non-minimal Higgs model of inflation with quartic non-minimal coupling between the Higgs field and gravity within the context of a realistic GUT gauge group based on supersymmetric $SU(4)_{C}\times SU(2)_{L}\times SU(2)_{R}$. These models are incorporated with a realistic scenario of reheating and non-thermal leptogenesis, compatible with the constraints from the baryon asymmetry of the universe. Notably, both models successfully address the MSSM $\mu$-problem and avoid the issue of primordial magnetic monopoles. Our analysis reveals that both models predict a scalar spectral index $n_s$ that closely aligns with the central observationally favored value of Planck2018 + BICEP2/Keck Array (BK15) data and yield a large tensor-to-scalar ratio ($r > 10^{-3}$), potentially detectable in forthcoming CMB experiments.