Unifying inflation with the axion, dark matter, baryogenesis and the seesaw mechanism

A minimal extension of the Standard Model (SM) with a single new mass scale and providing a complete and consistent picture of particle physics and cosmology up to the Planck scale is presented. We add to the SM three right-handed SM-singlet neutrinos, a new vector-like color triplet fermion and a complex SM singlet scalar $\sigma$ that stabilises the Higgs potential and whose vacuum expectation value at $\sim 10^{11}$ GeV breaks lepton number and a Peccei-Quinn symmetry simultaneously. Primordial inflation is produced by a combination of $\sigma$ (non-minimally coupled to the scalar curvature) and the SM Higgs. Baryogenesis proceeds via thermal leptogenesis. At low energies, the model reduces to the SM, augmented by seesaw-generated neutrino masses, plus the axion, which solves the strong CP problem and accounts for the dark matter in the Universe. The model predicts a minimum value of the tensor-to-scalar ratio $r\simeq 0.004$, running of the scalar spectral index $\alpha\simeq - 7\times 10^{-4}$, the axion mass $m_A\sim 100\,\mu{\rm eV}$ and cosmic axion background radiation corresponding to an increase of the effective number of relativistic neutrinos of $\sim 0.03$. It can be probed decisively by the next generation of cosmic microwave background and axion dark matter experiments.