Gravity waves and proton decay in a flipped SU(5) hybrid inflation model

Abstract

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