Gravity Waves and Proton Decay in Flipped SU(5) Hybrid Inflation Model

We revisit supersymmetric hybrid inflation in the context of flipped $SU(5)$ model. With minimal superpotential and minimal K"ahler potential, and soft SUSY masses of order $(1-100)$ TeV, compatibility with the Planck data yields a symmetry breaking scale $M$ of flipped $SU(5)$ close to $(2 - 4) \times 10^{15}$GeV\mathrm{.}Thisdisagreeswiththelowerlimit$M \gtrsim 7 \times 10^{15}$ GeV set from proton decay searches by the Super-Kamiokande collaboration. We show how $M$ close to the unification scale $2\times {10}^{16}$ GeV can be reconciled with SUSY hybrid inflation by employing a non-minimal K"ahler potential. Proton decays into $e^{+}{\pi }^0$ with an estimated lifetime of order ${10}^{36}$ years. The tensor to scalar ratio $r$ in this case can approach observable values $\sim {10}^{-4}-{10}^{-3}$.