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.
