<math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> axion model with observable proton decay

We propose a SU(5)&#215;U(1)X&#215;U(1)PQ model, where U(1)X is the generalization of the B−L (baryon minus lepton number) gauge symmetry and U(1)PQ is the global Peccei-Quinn (PQ) symmetry. There are four fermions families in 5&#175;+10 representations of SU(5), a mirror family in 5+10&#175; representations, and three SU(5) singlet Majorana fermions. The U(1)X related anomalies all cancel in the presence of the Majorana neutrinos. The SU(5) symmetry is broken at MGUT≃(6–9)&#215;1015 GeV and the proton lifetime τp is estimated to be well within the expected sensitivity of the future hyper-Kamiokande experiment, τp≲1.3&#215;1035 years. The SU(5) breaking also triggers the breaking of the PQ symmetry, resulting in axion dark matter (DM), with the axion decay constant fa of order MGUT or somewhat larger. The CASPEr experiment can search for such an axion DM candidate. The Hubble parameter during inflation must be low, Hinf≲109 GeV, in order to successfully resolve the axion domain wall, axion DM isocurvature and SU(5) monopole problems. With the identification of the U(1)X breaking Higgs field with the inflaton field, we implement inflection-point inflation, which is capable of realizing the desired value for Hinf. The vectorlike fermions in the model are essential for achieving successful unification of the SM gauge couplings as well as the phenomenological viability of both axion DM and inflation scenario.