A Pati-Salam Version of Subcritical Hybrid Inflation

Abstract

In this paper we present a model of subcritical hybrid inflation with a Pati-Salam [PS] symmetry group. Both the inflaton and waterfall fields contribute to the necessary e-foldings of inflation, while only the waterfall field spontaneously breaks PS hence monopoles produced during inflation are diluted during the inflationary epoch. The model is able to produce a tensor-to-scalar ratio, $r<0.09$ consistent with the latest BICEP2/Keck and Planck data, as well as scalar density perturbations and spectral index, $n_s$, consistent with Planck data. For particular values of the parameters, we find $r=0.084$ and $n_s=0.0963$. The energy density during inflation is directly related to the PS breaking scale, $v_{PS}$. The model also incorporates a ${\mathbb{Z}}_4^R$ symmetry which can resolve the $\mu$ problem and suppress dimension 5 operators for proton decay, leaving over an exact $R$-parity. Finally the model allows for a complete three family extension with a $D_4$ family symmetry which reproduces low energy precision electroweak and LHC data.

Comments: 19 pages, 4 figures. v2: typo fixed, figure added, references added; v3: additional typos fixed