Primordial monopoles, proton decay, gravity waves and GUT inflation

We consider non-supersymmetric GUT inflation models in which intermediate mass monopoles may survive inflation because of the restricted number of e-foldings experienced by the accompanying symmetry breaking. Thus, an observable flux of primordial magnetic monopoles, comparable to or a few orders below the Parker limit, may be present in the galaxy. The mass scale associated with the intermediate symmetry breaking is $10^{13}$ GeV for an observable flux level, with the corresponding monopoles an order of magnitude or so heavier. Examples based on $SO(10)$ and $E_6$ yield such intermediate mass monopoles carrying respectively two and three units of Dirac magnetic charge. For GUT inflation driven by a gauge singlet scalar field with a Coleman-Weinberg or Higgs potential, compatibility with the Planck measurement of the scalar spectral index yields a Hubble constant (during horizon exit of cosmological scales) $H \sim 7$--$9\times10^{13}$ GeV, with the tensor to scalar ratio $r$ predicted to be $\gtrsim0.02$. Proton lifetime estimates for decays mediated by the superheavy gauge bosons are also provided.